Homology, Homotopy and Applications

Volume 20 (2018)

Number 2

Decomposing manifolds into Cartesian products

Pages: 1 – 10

DOI: https://dx.doi.org/10.4310/HHA.2018.v20.n2.a1

Authors

Slawomir Kwasik (Department of Mathematics, Tulane University, New Orleans, Louisiana, U.S.A.)

Reinhard Schultz (Department of Mathematics, University of California at Riverside)

Abstract

The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we show that similar analogs do not exist unless one imposes further restrictions such as simple connectivity.

Keywords

Seifert manifold, Whitehead torsion, $s$-cobordism, surgery group

2010 Mathematics Subject Classification

57M50, 57R80

Full Text (PDF format)

Received 25 May 2017

Received revised 29 November 2017

Published 20 March 2018