2020/11/09 by Sam Nariman, Nariman, Sam
Mathematics · #53D10 #57Q35 #57R19 #57R32 #57R40 #57R50 #57R52 #57R65 #58D05 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2011.04156
openalex publication_date 2020/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we generalize the original idea of Thurston for the so called Mather-Thurston's theorem for foliated bundles to prove new variants of this theorem for PL homeomorphisms, contactormorphisms. These versions answer questions posed by Gelfand -Fuks and Greenberg on PL foliations and Rybicki on contactomorphisms. The interesting point about the original Thurston's technique compared to the better known Segal-McDuff's proof of the Mather-Thurston theorem is that it gives a compactly supported c-principle theorem without knowing the relevant local statement on open balls. In the appendix, we show that Thurston's fragmentation implies the non-abelian Poincare duality theorem and its generalization using blob complexes.