Articoli correlati a Introduction to Algebraic Topology: 119
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A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.
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Contenuti
0 Introduction.- Notation.- Brouwer Fixed Point Theorem.- Categories and Functors.- 1.Some Basic Topological Notions.- Homotopy.- Convexity, Contractibility, and Cones.- Paths and Path Connectedness.- 2 Simplexes.- Affine Spaces.- Affine Maps.- 3 The Fundamental Group.- The Fundamental Groupoid.- The Functor ?1.- ?1(S1).- 4 Singular Homology.- Holes and Green’s Theorem.- Free Abelian Groups.- The Singular Complex and Homology Functors.- Dimension Axiom and Compact Supports.- The Homotopy Axiom.- The Hurewicz Theorem.- 5 Long Exact Sequences.- The Category Comp.- Exact Homology Sequences.- Reduced Homology.- 6 Excision and Applications.- Excision and Mayer-Vietoris.- Homology of Spheres and Some Applications.- Barycentric Subdivision and the Proof of Excision.- More Applications to Euclidean Space.- 7 Simplicial Complexes.- Definitions.- Simplicial Approximation.- Abstract Simplicial Complexes.- Simplicial Homology.- Comparison with Singular Homology.- Calculations.- Fundamental Groups of Polyhedra.- The Seifert-van Kampen Theorem.- 8 CW Complexes.- Hausdorff Quotient Spaces.- Attaching Cells.- Homology and Attaching Cells.- CW Complexes.- Cellular Homology.- 9 Natural Transformations.- Definitions and Examples.- Eilenberg-Steenrod Axioms.- Chain Equivalences.- Acyclic Models.- Lefschetz Fixed Point Theorem.- Tensor Products.- Universal Coefficients.- Eilenberg-Zilber Theorem and the Künneth Formula.- 10 Covering Spaces.- Basic Properties.- Covering Transformations.- Existence.- Orbit Spaces.- 11 Homotopy Groups.- Function Spaces.- Group Objects and Cogroup Objects.- Loop Space and Suspension.- Homotopy Groups.- Exact Sequences.- Fibrations.- A Glimpse Ahead.- 12 Cohomology.- Differential Forms.- Cohomology Groups.- Universal Coefficients Theorems for Cohomology.- Cohomology Rings.- Computations and Applications.- Notation.
Product Description
Book by Rotman Joseph J
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- EditoreSpringer Verlag
- Data di pubblicazione1998
- ISBN 10 0387966781
- ISBN 13 9780387966786
- RilegaturaCopertina rigida
- LinguaInglese
- Numero di pagine456
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An Introduction to Algebraic Topology (Graduate Texts in Mathematics, 119)
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An Introduction to Algebraic Topology: 119 (Graduate Texts in Mathematics, 119)
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Hardback. Condizione: Fair. A readable copy of the book which may include some defects such as highlighting and notes. Cover and pages may be creased and show discolouration. Codice articolo GOR014246116
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An Introduction to Algebraic Topology (Graduate Texts in Mathematics, 119)
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Introduction to Algebraic Topology
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An Introduction to Algebraic Topology
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced. 456 pp. Englisch. Codice articolo 9780387966786
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An Introduction to Algebraic Topology (Graduate Texts in Mathematics, 119)
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An Introduction to Algebraic Topology (Graduate Texts in Mathematics, 119)
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Introduction to Algebraic Topology
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An Introduction to Algebraic Topology
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Springer New York, Springer New York, 1988
ISBN 10: 0387966781
ISBN 13: 9780387966786
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - There is a canard that every textbook of algebraic topology either ends with the definition of the Klein bottle or is a personal communication to J. H. C. Whitehead. Of course, this is false, as a glance at the books of Hilton and Wylie, Maunder, Munkres, and Schubert reveals. Still, the canard does reflect some truth. Too often one finds too much generality and too little attention to details. There are two types of obstacle for the student learning algebraic topology. The first is the formidable array of new techniques (e. g. , most students know very little homological algebra); the second obstacle is that the basic defini tions have been so abstracted that their geometric or analytic origins have been obscured. I have tried to overcome these barriers. In the first instance, new definitions are introduced only when needed (e. g. , homology with coeffi cients and cohomology are deferred until after the Eilenberg-Steenrod axioms have been verified for the three homology theories we treat-singular, sim plicial, and cellular). Moreover, many exercises are given to help the reader assimilate material. In the second instance, important definitions are often accompanied by an informal discussion describing their origins (e. g. , winding numbers are discussed before computing 1tl (Sl), Green's theorem occurs before defining homology, and differential forms appear before introducing cohomology). We assume that the reader has had a first course in point-set topology, but we do discuss quotient spaces, path connectedness, and function spaces. Codice articolo 9780387966786
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An Introduction to Algebraic Topology
Editore:
Springer-Verlag New York Inc., 1988
ISBN 10: 0387966781
ISBN 13: 9780387966786
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Da: THE SAINT BOOKSTORE, Southport, Regno Unito
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Hardback. Condizione: New. This item is printed on demand. New copy - Usually dispatched within 5-9 working days 847. Codice articolo C9780387966786
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