PL homeomorphisms of surfaces and codimension 2 PL foliations

2022/07/11 by Nariman, Sam
#55R40 #57Q60 #57R30 #57R32 #58D05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2207.04936

Abstract

Haefliger-Thurston's conjecture predicts that Haefliger's classifying space for C^r-foliations of codimension n whose normal bundles are trivial is 2n-connected. In this paper, we confirm this conjecture for PL foliations of codimension 2. As a consequence, we use a version of Mather-Thurston's theorem for PL homeomorphisms due to the author to derive new homological properties for PL surface homeomorphisms. In particular, we answer a question of Epstein in dimension 2 and prove the simplicity of the identity component of PL surface homeomorphisms.

Related

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• On flat manifold bundles and the connectivity of Haefliger's classifying spaces
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• Thurston's fragmentation and c-principles
• Foliation surgeries and the concordance groups of foliated spheres