Manifolds with involution whose fixed point set \(F\) has the property \(W(F)=1\)
type: Item
instance of: scholarly article
title: Manifolds with involution whose fixed point set \(F\) has the property \(W(F)=1\)
zbMATH Open document ID: 0743.57021
author: Zhende Wu
published in: Chinese Science Bulletin
publication date: 1992-06-26T00:00:00Z
review text: This paper attempts to determine the possible cobordism classes of involutions for which the fixed set has trivial Stiefel-Whitney class. Unfortunately, the proof is completely inadequate. The main technical points needed are given in Lemma 1 and the assertions made there all require verification. The classes \(A\) used are elements of the bordism ring, and are not easily seen to be in \(\mathbb{Z}/2\mathbb{Z}\). The equation derived from that only holds up to bordism and it is far from clear that the integers \(i\) must be of the form \(2^ s-1\). Finally, it appears that Lemma 1 needs to be strengthened in order to apply in the proof of the Theorem --- more than one s-number may be nonzero, and one must consider sums of classes.
Mathematics Subject Classification ID: 57R85
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 21570
zbMATH Keywords: fixed set with trivial Stiefel-Whitney class
zbMATH Keywords: cobordism classes of involutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 21570