Degree-one maps onto lens spaces

Claude Hayat-Legrand, Shicheng Wang and Heiner Zieschang

Vol. 176 (1996), No. 1, 19–32

DOI: 10.2140/pjm.1996.176.19

Abstract

The paper deals with the question about the existence or non-existence of a degree-one map of a closed orientable 3-manifold M to some lens space. The answer to this question is determined by the cyclic decomposition of H₁(M), except when H₁(M) contains an even number of direct factors isomorphic to Z_2^k. In this case one has to calculate the linking matrix of M to get the answer. For every n even, we give a Seifert manifold M_n with H₁(M_n)≅Z_n ⊕Z_n that does not admit a degree-one map to L(n,m) for any m.

Mathematical Subject Classification 2000

Primary: 57N10

Secondary: 57M25

Milestones

Received: 15 February 1994

Revised: 18 May 1994

Published: 1 November 1996