Deficiencies of smooth manifolds
type: Item
instance of: scholarly article
title: Deficiencies of smooth manifolds
zbMATH Open document ID: 0573.57020
DOI: 10.1016/0166-8641(85)90069-0
published in: Topology and its Applications
publication date: 1985-01-01T00:00:00Z
review text: For a given closed manifold \(M^ n\), there are involutions \((X^{2n},T)\) on closed manifolds having the fixed point set M, which give us the integers \[ \delta (M,X)=\{\dim H^*(X;{\mathbb{Z}}_ 2)-\dim H^*(M;{\mathbb{Z}}_ 2)\}/2\geq 0; \] and the deficiency \(\eta\) (M) due to Kulkarni is the minimum of all \(\delta\) (M,X). This paper exhibits manifolds M for which \(\eta (M)>0\), and studies general conditions under which \(\delta (M,X)>0\) for any such involution (X,T) whose normal bundle to the fixed point set is the tangent bundle of M.
Mathematics Subject Classification ID: 57S17
zbMATH DE Number: 3915257
zbMATH Keywords: involutions
zbMATH Keywords: deficiency
zbMATH Keywords: fixed point set
author: R. E. Stong
MaRDI profile type: Publication
full work available at URL: 0166-8641(85)90069-0
OpenAlex ID: W2047301452
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Wikidata QID: Q127191008
description: scientific article; zbMATH DE number 3915257