TL;DR
This paper introduces a novel integral lift of the Gamma-genus for complex-oriented manifolds, utilizing a family of deformations of the Dirac operator parametrized by Sp/U, extending the classical genus.
Contribution
It constructs a new ring-homomorphism for the Gamma-genus via deformations of the Dirac operator, providing a deeper geometric and algebraic understanding.
Findings
Defined a ring-homomorphism lifting the Gamma-genus
Connected the Gamma-genus to deformations of Dirac operators
Extended the classical Gamma-genus to a new integral context
Abstract
The Hirzebruch genus of complex-oriented manifolds associated to the Gamma-function lifts to a ring-homomorphism defined by a family of deformations of the Dirac operator, parametrized by the homogeneous space Sp/U.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry