Involution number sequence and dimensions of the components in fixed point set of an involution. II
type: Item
instance of: scholarly article
title: Involution number sequence and dimensions of the components in fixed point set of an involution. II
zbMATH Open document ID: 0790.57025
author: Huajian Yang
author: Zhende Wu
author: Zongze Liu
published in: Science in China. Series A
publication date: 1993-01-17T00:00:00Z
review text: [For Part I see ibid. 34, No. 11, 1302-1306 (1991; Zbl 0784.57021).] The authors prove: Given any smooth unfree involution on \((S^ 1)^ n\) the fixed-point set of the involution must be constant dimensional. In order to show this they compute the total Stiefel-Whitney classes \(W(\mathbb{R}^ m (\tau))\) by comparing them with \(W(\mathbb{R}^ m (\tau_ i))\), where \(\tau\) is the given involution and \(\tau_ i\), \(i=1,\dots,n\), are particular involutions on \((S^ 1)^ n\). Finally the computation of \(W(\overline T_ m (S^ 1)^ n)\), where \(\overline T_ m (S^ 1)^ n\) is the tangent bundle along the fibre of \(\mathbb{R}^ m (\tau)\), leads to the result.
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 57S17
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 98076
zbMATH Keywords: Leray-Hirsch theorem
zbMATH Keywords: smooth unfree involution on \((S^ 1)^ n\)
zbMATH Keywords: fixed- point set
zbMATH Keywords: total Stiefel-Whitney classes
reviewed by: Daciberg Lima Gonçalves
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 98076