Equivariant cobordism, vector fields, and the Euler characteristic
type: Item
instance of: scholarly article
title: Equivariant cobordism, vector fields, and the Euler characteristic
zbMATH Open document ID: 0571.57025
published in: Journal of the Mathematical Society of Japan
publication date: 1986-01-01T00:00:00Z
review text: Let G be a finite group. For two closed G-manifolds M and N, a G- cobordism L between them is called a Reinhart G-cobordism if L admits a G-invariant nonzero vector field which is inward normal on M and outward normal on N. The aim of this paper is to obtain a necessary and sufficient condition for the existence of a Reinhart G-cobordism between two given G-cobordant closed G-manifolds. \textit{B. L. Reinhart} [Topology 2, 173-177 (1963; Zbl 0178.264)] is just the case in which G is the trivial group. When G is of odd order or of order 2, the author gives such a condition in terms of the Euler characteristic of fixed point sets with specified normal representations. The result is proved by altering a given G-cobordism to a Reinhart G-cobordism by equivariant surgery and connected sum. If G is of order 2, \textit{R. E. Stong} [Math. Ann. 26, 181- 196 (1975; Zbl 0303.57016)] obtained such a condition in some cases.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 3911318
zbMATH Keywords: actions of finite groups
zbMATH Keywords: equivariant cobordism
zbMATH Keywords: Reinhart G-cobordism
zbMATH Keywords: Euler characteristic of fixed point sets
zbMATH Keywords: equivariant surgery
author: Katsuhiro Komiya
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/03810009
OpenAlex ID: W2054589201
DOI: 10.2969/JMSJ/03810009
description: scientific article; zbMATH DE number 3911318