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2020 Simplifying Weinstein Morse functions
Oleg Lazarev
Geom. Topol. 24(5): 2603-2646 (2020). DOI: 10.2140/gt.2020.24.2603

Abstract

We prove that the minimum number of critical points of a Weinstein Morse function on a Weinstein domain of dimension at least six is at most two more than the minimum number of critical points of a smooth Morse function on that domain; if the domain has nonzero middle-dimensional homology, these two numbers agree. There is also an upper bound on the number of gradient trajectories between critical points in smoothly trivial Weinstein cobordisms. As an application, we show that the number of generators for the Grothendieck group of the wrapped Fukaya category is at most the number of generators for singular cohomology and hence vanishes for any Weinstein ball. We also give a topological obstruction to the existence of finite-dimensional representations of the Chekanov–Eliashberg DGA for Legendrians.

Citation

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Oleg Lazarev. "Simplifying Weinstein Morse functions." Geom. Topol. 24 (5) 2603 - 2646, 2020. https://doi.org/10.2140/gt.2020.24.2603

Information

Received: 8 May 2019; Revised: 7 November 2019; Accepted: 9 December 2019; Published: 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194299
Digital Object Identifier: 10.2140/gt.2020.24.2603

Subjects:
Primary: 57R17
Secondary: 53D37, 53D40, 57R80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.24 • No. 5 • 2020
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