The Morse-Bott inequalities, orientations, and the Thom isomorphism in Morse homology

被引：1

作者：

Rot, Thomas O. ^{[1
]}

机构：

[1] Univ Cologne, Math Inst, Weyertal 86-90, D-50931 Cologne, Germany

来源：

COMPTES RENDUS MATHEMATIQUE | 2016年 / 354卷 / 10期

关键词：

D O I：

10.1016/j.crma.2016.08.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Morse-Bott inequalities relate the topology of a closed manifold to the topology of the critical point set of a Morse-Bott function defined on it. The Morse-Bott inequalities are sometimes stated under incorrect orientation assumptions. We show that these assumptions are insufficient with an explicit counterexample and clarify the origin of the mistake. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

引用

页码：1026 / 1028

页数：3

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