Year: 2024
Type: article
Abstract: The Haefliger–Thurston 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 piecewise linear (PL) foliations of codimension $2$ . Using this, we use a version of the Mather–Thurston theorem for PL homeomorphisms due to the author to derive new homological properties for PL surface homeomorphisms. In particular, we answer the question of Epstein in dimension $2$ and prove the simplicity of the identity component of PL surface homeomorphisms.
Source: Compositio Mathematica
Author: Sam Nariman
Institution: Purdue University West Lafayette
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
Funder: National Science Foundation
OpenAlex ID: W4405689120