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…
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3 results for “Thurston-Winkelnkemper”
Given an open book decomposition of a three manifold , Thurston and Winkelnkemper [TW] construct a specific contact form on . Given a spin-c Dirac operator on , the contact form naturally associates a one parameter family of Dirac operators $D_r = D - \frac{ir}{2}\cl(a)$ for . When $r>>…
Paper proves unique contact structure supported by positive flow-spines.
problem Existence and uniqueness of contact structures on 3-manifolds.
method Introduces positivity condition for flow-spines and proves existence and uniqueness of contact structures.
result Any positive flow-spine of a closed, connected, oriented 3-manifold supports a unique contact structure up to isotopy.