Several new Witten rigidity theorems for spin^c manifolds

2025/12/18 by Jianyun Guan, Kefeng Liu, Guan, Jianyun +3
Mathematics · #Geometric and Algebraic Topology #Advanced Operator Algebra Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2512.16088

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^c manifolds and twisted Toeplitz operators on odd-dimensional spin^c manifolds with circle actions.

Citations

• Several new Witten rigidity theorems for elliptic genus
• SL(2,Z) modular forms and Witten genus in odd dimensions
• SL(2,Z) Modular Forms and Anomaly Cancellation Formulas II
• SL(2,Z) modular forms and anomaly cancellation formulas
• On the Witten Rigidity Theorem for Odd Dimensional Manifolds
• On Family Rigidity Theorems I

Related

• Several new Witten rigidity theorems for elliptic genus
• On the Witten Rigidity Theorem for Odd Dimensional Manifolds
• Rigidity and Vanishing Theorems on ℤ/k Spin^c manifolds
• On Family Rigidity Theorems II
• SL(2,Z) modular forms and Witten genus in odd dimensions