Spin/pin-structures And Real Enumerative Geometry - Rilegato

Chen, Xujia; Zinger, Aleksey

 
9789811278532: Spin/pin-structures And Real Enumerative Geometry
Rilegato
ISBN 10: 9811278539 ISBN 13: 9789811278532
Casa editrice: WSPC, 2023

Sinossi

Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the foundation for the original proof of the renowned Atiyah–Singer Index Theory. More recently, they have underpinned the symplectic topology foundations of the so-called real sector of the mirror symmetry of string theory. This semi-expository three-part monograph provides an accessible introduction to Spin- and Pin-structures in general, demonstrates their role in the orientability considerations in symplectic topology, and presents their applications in enumerative geometry. Part I contains a systematic treatment of Spin/Pin-structures from different topological perspectives and may be suitable for an advanced undergraduate reading seminar. This leads to Part II, which systematically studies orientability problems for the determinants of real Cauchy–Riemann operators on vector bundles. Part III introduces enumerative geometry of curves in complex projective varieties and in symplectic manifolds, demonstrating some applications of the first two parts in the process. Two appendices review the Čech cohomology perspective on fiber bundles and Lie group covering spaces.

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Editore
WSPC
Data di pubblicazione
2023
Lingua
Inglese
ISBN 10 
9811278539
ISBN 13 
9789811278532
Rilegatura
Copertina rigida
Numero di pagine
468
Contatto del produttore
non disponibile
Persona responsabile
gpsr@libri.de
gpsr@libri.de

Friedensallee 273
Hamburg
22763
Germania