Several new Witten rigidity theorems for spin$^c$ manifolds
Jianyun Guan, Kefeng Liu, Yong Wang
TL;DR
This paper proves new Witten rigidity theorems for spin$^c$ manifolds, extending previous modular invariance methods to generalized Witten genus and Toeplitz operators with circle actions.
Contribution
It introduces novel rigidity results for twisted Dirac operators and Toeplitz operators on spin$^c$ manifolds using advanced modular invariance techniques.
Findings
New rigidity theorems for generalized Witten genus
Rigidity results for twisted Toeplitz operators
Extension of Liu's and Han-Yu's methods
Abstract
Using Liu's modular invariance method and its odd-dimensional extension by Han and Yu, we establish new Witten rigidity theorems for the generalized Witten genus of twisted Dirac operators on even-dimensional spin manifolds and twisted Toeplitz operators on odd-dimensional spin manifolds with circle actions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Geometric Analysis and Curvature Flows