Cobordism group of Morse functions on manifolds
type: Item
instance of: scholarly article
title: Cobordism group of Morse functions on manifolds
zbMATH Open document ID: 1064.57037
author: Kazuichi Ikegami
published in: Hiroshima Mathematical Journal
publication date: 2005-02-28T00:00:00Z
review text: This paper defines and computes oriented and unoriented cobordism of manifolds with Morse functions. The equivalence relation assumes the cobordism is mapped into \(\mathbb{R}\times [0,1]\) with only fold singularities. The results say that the cobordism groups are direct sums of ordinary cobordism and copies of \(\mathbb{Z}\). The extra integer invariants are given by the indices of the critical points of the Morse function. For the oriented case of manifolds of dimension \(4k+1\), there is an extra invariant given by the difference between the semicharacteristic of \(M\) and a semicharacteristic computed from the Morse function.
Mathematics Subject Classification ID: 57R90
Mathematics Subject Classification ID: 57R75
Mathematics Subject Classification ID: 57R70
zbMATH DE Number: 2139567
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.32917/hmj/1150998163
OpenAlex ID: W1597345065
Wikidata QID: Q128870386
DOI: 10.32917/HMJ/1150998163
description: scientific article; zbMATH DE number 2139567