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Approximating a topological section by a piecewise-linear section

Colin Rourke
Algebraic & Geometric Topology 16 (2016) 1373–1377
DOI: 10.2140/agt.2016.16.1373
Abstract

In answer to a question from János Kollár, we prove that a surjective piecewise-linear map with a topological section admits a nearby homotopic piecewise-linear section.

Keywords
section, topological section, PL approximation
Mathematical Subject Classification 2010
Primary: 57Q55
Secondary: 57Q05, 57Q37
References
Publication
Received: 31 January 2014
Revised: 10 September 2015
Accepted: 13 September 2015
Published: 1 July 2016
Authors
Colin Rourke
Mathematics Institute
University of Warwick
Coventry CV4 7AL
UK
http://msp.warwick.ac.uk/~cpr