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portada Spin/Pin-Structures and Real Enumerative Geometry
Type
Physical Book
Author
Publisher
Language
English
Pages
468
Format
Hardcover
Dimensions
22.9x15.2x2.5 cm
Weight
0.79 kg.
ISBN13
9789811278532
Categories

Spin/Pin-Structures and Real Enumerative Geometry

Xujia Chen (Author) · Aleksey Zinger (Author) · World Scientific Publishing Company · Hardcover

Spin/Pin-Structures and Real Enumerative Geometry - Chen, Xujia ; Zinger, Aleksey

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Synopsis "Spin/Pin-Structures and Real Enumerative Geometry"

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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