36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

"PL homeomorphisms of surfaces and codimension 2 PL foliations"

Nariman, Sam

Haefliger-Thurston's conjecture predicts that Haefliger's classifying space for codimension $n$ smooth foliations whose normal bundles are trivial is $2n$-connected. In this talk, we discuss how one can use Greenberg's model to confirm this conjecture for codimension $2$ PL foliations. As a consequence, we use our version of Mather-Thurston's theorem for PL homeomorphisms to derive new homological properties for PL surface homeomorphisms. In particular, we answer a question of Epstein regarding the simplicity of the identity component of PL surface homeomorphisms.

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