Geodesic
$\operatorname{PL}(M)$ admits no Polish group topology
Kathryn Mann1
1 Department of Mathematics University of California Berkeley, CA 94720, U.S.A.
Fundamenta Mathematicae, Tome 238 (2017) no. 3, pp. 285-295 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that the group of piecewise linear homeomorphisms of any compact PL manifold does not admit a Polish group topology, using both general results on topologies on groups of homeomorphisms, and results on the algebraic structure of PL homeomorphism groups. The proof also shows that the group of piecewise projective homeomorphisms of $S^1$ has no Polish topology.
DOI : 10.4064/fm285-10-2016
Keywords: group piecewise linear homeomorphisms compact manifold does admit polish group topology using general results topologies groups homeomorphisms results algebraic structure homeomorphism groups proof shows group piecewise projective homeomorphisms has polish topology

Kathryn Mann 1

1 Department of Mathematics University of California Berkeley, CA 94720, U.S.A. 
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Kathryn Mann. $\operatorname{PL}(M)$ admits no Polish group topology. Fundamenta Mathematicae, Tome 238 (2017) no. 3, pp. 285-295. doi: 10.4064/fm285-10-2016

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