Several new Witten rigidity theorems for elliptic genus
Jianyun Guan, Kefeng Liu, Yong Wang
TL;DR
This paper proves new Witten rigidity theorems for elliptic genus in spin manifolds, extending previous results to twisted Dirac and Toplitz operators under circle actions.
Contribution
It introduces novel rigidity theorems for elliptic genus of twisted Dirac and Toplitz operators, expanding the scope of Witten's rigidity in spin manifolds.
Findings
Proved Witten rigidity for twisted Dirac operators in even dimensions.
Established Witten rigidity for twisted Toplitz operators in odd dimensions.
Derived several new rigidity theorems for elliptic genus.
Abstract
Using the Liu's method, we prove a new Witten rigidity theorem of elliptic genus of twisted Dirac operators in even dimensional spin manifolds under the circle action. Combined with the Han-Yu's method, we prove the Witten rigidity theorems of elliptic genus of twisted Toplitz operators of odd-dimensional spin manifolds under the circle action. Moreover, we have obtained several similar Witten rigidity theorems of elliptic genus.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Polynomial and algebraic computation · Algebraic Geometry and Number Theory