Classifying involutions on \(PR(2k)\) up to equivariant cobordism
type: Item
instance of: scholarly article
title: Classifying involutions on \(PR(2k)\) up to equivariant cobordism
zbMATH Open document ID: 0785.57014
DOI: 10.1007/BF02731958
author: Huajian Yang
author: Zhende Wu
author: Zongze Liu
published in: Chinese Annals of Mathematics. Series B
publication date: 1994-04-21T00:00:00Z
review text: The main result of this paper is that up to equivariant bordism, every involution \((RP(2k),T)\) on an even projective space is equivalent to one of the standard linear involutions \(T_ i([x_ 0,\dots,x_{2k}])= [- x_ 0,\dots,-x_ i, x_{i+1},\dots, x_{2k}]\) with \(-1\leq i\leq k- 1\), where \(T_{-1}\) = identity. While the proof given here is based entirely on bordism methods, the result is an immediate consequence of Smith theory. It is well-known that the fixed set of any involution on \(RP(2k)\) has the same \(\text{mod} 2\) cohomology as one of the linear examples.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 55N22
zbMATH DE Number: 205748
zbMATH Keywords: equivariant bordism
zbMATH Keywords: involution
zbMATH Keywords: projective space
zbMATH Keywords: Smith theory
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02731958
OpenAlex ID: W2142549810
description: scientific article; zbMATH DE number 205748