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September 2014 Asymptotic spectral flow for Dirac operators of disjoint Dehn twists
Chung-Jun Tsai
Asian J. Math. 18(4): 633-686 (September 2014).


Let $Y$ be a compact, oriented 3-manifold with a contact form $a$. For any Dirac operator $\mathcal{D}$, we study the asymptotic behavior of the spectral flow between $\mathcal{D}$ and $\mathcal{D} + \mathrm{cl}(-\frac{ir}{2}a)$ as $r \to \infty$. 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 $\mathcal{O}(r)$.


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Chung-Jun Tsai. "Asymptotic spectral flow for Dirac operators of disjoint Dehn twists." Asian J. Math. 18 (4) 633 - 686, September 2014.


Published: September 2014
First available in Project Euclid: 6 November 2014

zbMATH: 1308.58014
MathSciNet: MR3275723

Primary: 53D35 , 58J30

Keywords: Dehn twist , Dirac spectral flow , open book decomposition

Rights: Copyright © 2014 International Press of Boston

Vol.18 • No. 4 • September 2014
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