Algebraic Topology: A First Course

Valutazione media 4
( su 4 valutazioni fornite da GoodReads )
 
9780387943275: Algebraic Topology: A First Course

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

I Calculus in the Plane.- 1 Path Integrals.- 1a. Differential Forms and Path Integrals.- 1b. When Are Path Integrals Independent of Path?.- 1c. A Criterion for Exactness.- 2 Angles and Deformations.- 2a. Angle Functions and Winding Numbers.- 2b. Reparametrizing and Deforming Paths.- 2c. Vector Fields and Fluid Flow.- II Winding Numbers.- 3 The Winding Number.- 3a. Definition of the Winding Number.- 3b. Homotopy and Reparametrization.- 3c. Varying the Point.- 3d. Degrees and Local Degrees.- 4 Applications of Winding Numbers.- 4a. The Fundamental Theorem of Algebra.- 4b. Fixed Points and Retractions.- 4c. Antipodes.- 4d. Sandwiches.- III Cohomology and Homology, I.- 5 De Rham Cohomology and the Jordan Curve Theorem.- 5a. Definitions of the De Rham Groups.- 5b. The Coboundary Map.- 5c. The Jordan Curve Theorem.- 5d. Applications and Variations.- 6 Homology.- 6a. Chains, Cycles, and H0U.- 6b. Boundaries, H1U, and Winding Numbers.- 6c. Chains on Grids.- 6d. Maps and Homology.- 6e. The First Homology Group for General Spaces.- IV Vector Fields.- 7 Indices of Vector Fields.- 7a. Vector Fields in the Plane.- 7b. Changing Coordinates.- 7c. Vector Fields on a Sphere.- 8 Vector Fields on Surfaces.- 8a. Vector Fields on a Torus and Other Surfaces.- 8b. The Euler Characteristic.- V Cohomology and Homology, II.- 9 Holes and Integrals.- 9a. Multiply Connected Regions.- 9b. Integration over Continuous Paths and Chains.- 9c. Periods of Integrals.- 9d. Complex Integration.- 10 Mayer—Vietoris.- 10a. The Boundary Map.- 10b. Mayer—Vietoris for Homology.- 10c. Variations and Applications.- 10d. Mayer—Vietoris for Cohomology.- VI Covering Spaces and Fundamental Groups, I.- 11 Covering Spaces.- 11a. Definitions.- 11b. Lifting Paths and Homotopies.- 11c. G-Coverings.- 11d. Covering Transformations.- 12 The Fundamental Group.- 12a. Definitions and Basic Properties.- 12b. Homotopy.- 12c. Fundamental Group and Homology.- VII Covering Spaces and Fundamental Groups, II.- 13 The Fundamental Group and Covering Spaces.- 13a. Fundamental Group and Coverings.- 13b. Automorphisms of Coverings.- 13c. The Universal Covering.- 13d. Coverings and Subgroups of the Fundamental Group.- 14 The Van Kampen Theorem.- 14a. G-Coverings from the Universal Covering.- 14b. Patching Coverings Together.- 14c. The Van Kampen Theorem.- 14d. Applications: Graphs and Free Groups.- VIII Cohomology and Homology, III.- 15 Cohomology.- 15a. Patching Coverings and ?ech Cohomology.- 15b. ?ech Cohomology and Homology.- 15c. De Rham Cohomology and Homology.- 15d. Proof of Mayer—Vietoris for De Rham Cohomology.- 16 Variations.- 16a. The Orientation Covering.- 16b. Coverings from 1-Forms.- 16c. Another Cohomology Group.- 16d. G-Sets and Coverings.- 16e. Coverings and Group Homomorphisms.- 16f. G-Coverings and Cocycles.- IX Topology of Surfaces.- 17 The Topology of Surfaces.- 17a. Triangulation and Polygons with Sides Identified.- 17b. Classification of Compact Oriented Surfaces.- 17c. The Fundamental Group of a Surface.- 18 Cohomology on Surfaces.- 18a. 1-Forms and Homology.- 18b. Integrals of 2-Forms.- 18c. Wedges and the Intersection Pairing.- 18d. De Rham Theory on Surfaces.- X Riemann Surfaces.- 19 Riemann Surfaces.- 19a. Riemann Surfaces and Analytic Mappings.- 19b. Branched Coverings.- 19c. The Riemann—Hurwitz Formula.- 20 Riemann Surfaces and Algebraic Curves.- 20a. The Riemann Surface of an Algebraic Curve.- 20b. Meromorphic Functions on a Riemann Surface.- 20c. Holomorphic and Meromorphic 1-Forms.- 20d. Riemann’s Bilinear Relations and the Jacobian.- 20e. Elliptic and Hyperelliptic Curves.- 21 The Riemann—Roch Theorem.- 21a. Spaces of Functions and 1-Forms.- 21b. Adeles.- 21c. Riemann—Roch.- 21d. The Abel—Jacobi Theorem.- XI Higher Dimensions.- 22 Toward Higher Dimensions.- 22a. Holes and Forms in 3-Space.- 22b. Knots.- 22c. Higher Homotopy Groups.- 22d. Higher De Rham Cohomology.- 22e. Cohomology with Compact Supports.- 23 Higher Homology.- 23a. Homology Groups.- 23b. Mayer—Vietoris for Homology.- 23c. Spheres and Degree.- 23d. Generalized Jordan Curve Theorem.- 24 Duality.- 24a. Two Lemmas from Homological Algebra.- 24b. Homology and De Rham Cohomology.- 24c. Cohomology and Cohomology with Compact Supports.- 24d. Simplicial Complexes.- Appendices.- Appendix A Point Set Topology.- A1. Some Basic Notions in Topology.- A2. Connected Components.- A3. Patching.- A4. Lebesgue Lemma.- Appendix B Analysis.- B1. Results from Plane Calculus.- B2. Partition of Unity.- Appendix C Algebra.- C1. Linear Algebra.- C2. Groups; Free Abelian Groups.- C3. Polynomials; Gauss’s Lemma.- Appendix D On Surfaces.- D1. Vector Fields on Plane Domains.- D2. Charts and Vector Fields.- D3. Differential Forms on a Surface.- Appendix E Proof of Borsuk’s Theorem.- Hints and Answers.- References.- Index of Symbols.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

I migliori risultati di ricerca su AbeBooks

Edizione Internazionale
Edizione Internazionale

1.

FULTON WILLIAM
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Brossura Quantità: 5
Edizione Internazionale
Da
bookscollection
(Delhi, DELHI, India)
Valutazione libreria
[?]

Descrizione libro Condizione libro: Brand New. PAPERBACK,Book Condition New, Brand New, Softcover, International Edition. We Do not Ship APO FPO AND PO BOX. Cover Image & ISBN may be different from US edition but contents as US Edition. Printing in English language. Quick delivery by USPS/UPS/DHL/FEDEX/ARAMEX ,Customer satisfaction guaranteed. We may ship the books from Asian regions for inventory purpose. Codice libro della libreria ABESTTND5328

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 15,92
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,60
Da: India a: U.S.A.
Destinazione, tempi e costi

2.

Fulton, William
Editore: Springer (1997)
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Quantità: 1
Da
Zubal-Books
(Cleveland, OH, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Springer, 1997. Condizione libro: New. 430 pp., Paperback, new. Codice libro della libreria ZB1054844

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 25,76
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,24
In U.S.A.
Destinazione, tempi e costi

3.

William Fulton
Editore: Springer-Verlag New York Inc., United States (1997)
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Paperback Quantità: 1
Da
The Book Depository US
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc., United States, 1997. Paperback. Condizione libro: New. 1st ed. 1995. Corr. 2nd printing 1997. 232 x 154 mm. Language: English . Brand New Book. To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups. Codice libro della libreria AAU9780387943275

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 35,91
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

4.

William Fulton
Editore: Springer-Verlag New York Inc., United States (1997)
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Paperback Quantità: 1
Da
The Book Depository
(London, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc., United States, 1997. Paperback. Condizione libro: New. 1st ed. 1995. Corr. 2nd printing 1997. 232 x 154 mm. Language: English . Brand New Book. To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups. Codice libro della libreria AAU9780387943275

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 36,14
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi
Edizione Internazionale
Edizione Internazionale

5.

Fulton
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Quantità: 2
Edizione Internazionale
Da
firstbookstore
(New Delhi, India)
Valutazione libreria
[?]

Descrizione libro Condizione libro: Brand New. Brand New Paperback International Edition, Perfect Condition. Printed in English. Excellent Quality, Service and customer satisfaction guaranteed!. Codice libro della libreria AIND-8293

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 39,08
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: India a: U.S.A.
Destinazione, tempi e costi
Edizione Internazionale
Edizione Internazionale

6.

Fulton
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Quantità: 2
Edizione Internazionale
Da
EBOOKSTORE2010
(New Delhi, ND, India)
Valutazione libreria
[?]

Descrizione libro Condizione libro: Brand New. New. SoftCover International edition. Different ISBN and Cover image but contents are same as US edition. Customer Satisfaction guaranteed!!. Codice libro della libreria SHUB99203

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 39,50
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: India a: U.S.A.
Destinazione, tempi e costi
Edizione Internazionale
Edizione Internazionale

7.

Fulton
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Quantità: 2
Edizione Internazionale
Da
Bookshub
(Karol Bagh, India)
Valutazione libreria
[?]

Descrizione libro Condizione libro: New. New. International edition. Perfect condition. Ship by express service to USA, Canada, Australia, France, Italy, UK, Germany and Netherland. Customer satisfaction our priority. Codice libro della libreria ABE-FEB-99203

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 39,54
Convertire valuta

Aggiungere al carrello

Spese di spedizione: GRATIS
Da: India a: U.S.A.
Destinazione, tempi e costi
Edizione Internazionale
Edizione Internazionale

8.

Fulton
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Paperback Quantità: 5
Edizione Internazionale
Da
PRIORITY BOOKS
(springfield, VA, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Paperback. Condizione libro: New. Softcover Book, Condition: New. 1st Edition. [Please Read Carefully Before Buying], This Is An International Edition. Printed In Black and White. , Book Cover And ISBN No May Be Different From US Edition. Restricted Sales Disclaimer Wordings Not For Sales In USA And Canada May Be Printed On The Cover Of The Book. Standard Shipping 7-14 Business Days. Expedited Shiping 4-8 Business Days. ***WE DO NOT ENTERTAIN BULK ORDERS.*** The Books May Be Ship From Overseas For Inventory Purpose. Codice libro della libreria 298385

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 36,28
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,70
In U.S.A.
Destinazione, tempi e costi
Edizione Internazionale
Edizione Internazionale

9.

Fulton
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Paperback Quantità: 1
Edizione Internazionale
Da
Nick Book House
(fresno, CA, U.S.A.)
Valutazione libreria
[?]

Descrizione libro Paperback. Condizione libro: New. New Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Codice libro della libreria 4080

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 36,37
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 3,70
In U.S.A.
Destinazione, tempi e costi

10.

William Fulton
Editore: Springer-Verlag New York Inc.
ISBN 10: 0387943277 ISBN 13: 9780387943275
Nuovi Paperback Quantità: 1
Da
THE SAINT BOOKSTORE
(Southport, Regno Unito)
Valutazione libreria
[?]

Descrizione libro Springer-Verlag New York Inc. Paperback. Condizione libro: new. BRAND NEW, Algebraic Topology: A First Course (1st ed. 1995. Corr. 2nd printing 1997), William Fulton, To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups. Codice libro della libreria B9780387943275

Maggiori informazioni su questa libreria | Fare una domanda alla libreria

Compra nuovo
EUR 33,52
Convertire valuta

Aggiungere al carrello

Spese di spedizione: EUR 6,87
Da: Regno Unito a: U.S.A.
Destinazione, tempi e costi

Vedi altre copie di questo libro

Vedi tutti i risultati per questo libro