Degree-one maps onto lens spaces
type: Item
instance of: scholarly article
title: Degree-one maps onto lens spaces
zbMATH Open document ID: 0877.57007
author: Claude Hayat-Legrand
author: Heiner Zieschang
author: Shicheng Wang
published in: Pacific Journal of Mathematics
publication date: 1997-06-23T00:00:00Z
review text: This paper shows that if \(M\) is a closed orientable 3-manifold then: (1) If there is a degree 1 map to \(L(n,m)\), then \(H_1(M)= Z_n\oplus A\). (2) If \(n>1\) is odd and \(H_1(M)= Z_n\oplus A\), there is a degree one map to an \(L(n,m)\) for some \(m\) with \(\text{gcd} (n,m)=1\). (3) If \(n=2^k(2j+1)\) and \(H_1(M)= Z_n\oplus A\), there is a degree one map to an \(L(n,m)\) for some \(m\) with \(\text{gcd} (n,m)=1\) provided \(A\) contains an even number of \(Z_2k\) summands. Examples are given to show that the assumption on \(A\) is needed for the third result.
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 55S37
zbMATH DE Number: 1025800
zbMATH Keywords: 3-manifold
zbMATH Keywords: degree 1 map
MaRDI profile type: Publication
full work available at URL: pjm.1996.176.19
OpenAlex ID: W1545027441
DOI: 10.2140/PJM.1996.176.19
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description: scientific article; zbMATH DE number 1025800