Dirac spectral flow on contact three manifolds II: Thurston--Winkelnkemper contact forms

Chung-Jun Tsai NTU

Differential Geometry mathscidoc:1909.10002

Given an open book decomposition (Σ,τ) of a three manifold Y , Thurston and Winkelnkemper [TW] construct a specific contact form a on Y . Given a spin-c Dirac operator D on Y , the contact form naturally associates a one parameter family of Dirac operators Dr = D− ir 2 cl(a) for r ≥ 0. When r >> 1, we prove that the spectrum of Dr = D0 − ir 2 cl(a) within [−1 2r 1 2 , 1 2r 1 2 ] are almost uniformly distributed. With the result in Part I [Ts1], it implies that the subleading order term of the spectral flow from D0 to Dr is of order r(logr) 9 2 . Besides the interests of the spectral flow, the method of this paper provide a tool to analyze the Dirac operator on an open book decomposition.
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@inproceedings{chung-jundirac,
  title={Dirac spectral flow on contact three manifolds II: Thurston--Winkelnkemper contact forms},
  author={Chung-Jun Tsai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190905135529790157487},
}
Chung-Jun Tsai. Dirac spectral flow on contact three manifolds II: Thurston--Winkelnkemper contact forms. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190905135529790157487.
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