Spin/Pin-Structures and Real Enumerative Geometry
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Book Overview Spin/Pin-structures on vector bundles have long featured prominently in differential geometry, in particular providing part of the founda...
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.
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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.
Book Details Format: Hardcover | Pages: 452 | Language: English | Publisher: WORLD SCIENTIFIC PUB CO INC | ISBN: 9811278539
FormatHardcover
Pages452
LanguageEnglish
ISBN9811278539
EAN9789811278532
PublisherWORLD SCIENTIFIC PUB CO INC
Publication Date1970-01-01
AccessoriesNo Accessory
ConditionNew
Product TypeHARD COVER BOOKS
Weight1.74 Pounds
Length9.0 Inches
Width6.0 Inches
Height1.0 Inches
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