简化Weinstein Morse函数

IF 2 1区 数学
Oleg Lazarev
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引用次数: 11

摘要

证明了在至少6维的Weinstein定义域上,Weinstein Morse函数的最小临界点数比光滑Morse函数的最小临界点数最多多2个;如果定义域具有非零的中维同调,则这两个数一致。作为一个推论,我们得到了域的包裹的Fukaya范畴的生成子数目的拓扑上界。我们还证明了在光滑平凡的温斯坦协体中临界点之间的梯度轨迹的数目有一个上界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Simplifying Weinstein Morse functions
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 non-zero middle-dimensional homology, these two numbers agree. As a corollary, we obtain a topological upper bound on the number of generators of the wrapped Fukaya category of the domain. We also show that there is an upper bound on the number of gradient trajectories between critical points in smoothly trivial Weinstein cobordisms.
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来源期刊
Geometry & Topology
Geometry & Topology 数学-数学
自引率
5.00%
发文量
34
期刊介绍: Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.
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