Geodesic
Approximating a topological section by a piecewise-linear section
Rourke, Colin1
1Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1373-1377
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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.

DOI : 10.2140/agt.2016.16.1373
Classification : 57Q55, 57Q05, 57Q37
Keywords: section, topological section, PL approximation

Rourke, Colin  1

1 Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK 
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Rourke, Colin. Approximating a topological section by a piecewise-linear section. Algebraic and Geometric Topology, Tome 16 (2016) no. 3, pp. 1373-1377. doi: 10.2140/agt.2016.16.1373

[1] J W Alexander, On the deformation of an n–cell, Proc. Nat. Acad. Sci. USA 9 (1923) 406

[2] M M Cohen, Simplicial structures and transverse cellularity, Ann. of Math. 85 (1967) 218

[3] A Hatcher, Algebraic topology, Cambridge Univ. Press (2002)

[4] C P Rourke, B J Sanderson, Introduction to piecewise-linear topology, 69, Springer (1972)

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