Asymptotic spectral flow for Dirac operators of disjoint Dehn twists

2011/04/26 by Chung-Jun Tsai, Tsai, Chung-Jun
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Spectral Theory in Mathematical Physics #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1104.5000

Various typos corrected

openalex publication_date 2011/04/26 · arxiv created 2013/07/08 · arxiv updated 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Y be a compact, oriented 3-manifold with a contact form a. For any Dirac operator D, we study the asymptotic behavior of the spectral flow between D and D+cl(-ira) as r very large. If a is the Thurston-Winkelnkemper contact form whose monodromy is the product of Dehn twists along disjoint circles, we prove that the next order term of the spectral flow function is of order r.

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