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  1. (, Forum of Mathematics, Sigma)
    Abstract 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 and contactormorphisms. These versions answer questions posed by Gelfand-Fuks ([GF73, Section 5]) and Greenberg ([Gre92]) on PL foliations and Rybicki ([Ryb10, Section 11]) 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 acompactly supportedc-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 ([MW12, Theorem 7.3.1]). To the memory of John Mather. 
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  2. (, Forum of mathematics Sigma)
    Free, publicly-accessible full text available April 28, 2026
  3. (, Notices of the AMS)
    Free, publicly-accessible full text available December 1, 2025
  4. (, Compositio Mathematica)
    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. 
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    Free, publicly-accessible full text available November 1, 2025
  5. (, Proceedings of the American Mathematical Society)
    We investigate a conjecture due to Haefliger and Thurston in the context of foliated manifold bundles. In this context, Haefliger-Thurston’s conjecture predicts that every M M -bundle over a manifold B B where dim ⁡<#comment/> ( B ) ≤<#comment/> dim ⁡<#comment/> ( M ) \operatorname {dim}(B)\leq \operatorname {dim}(M) is cobordant to a flat M M -bundle. In particular, we study the bordism class of flat M M -bundles over low dimensional manifolds, comparing a finite dimensional Lie group G G with D i f f 0 ( G ) \mathrm {Diff}_0(G) . 
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    Free, publicly-accessible full text available November 1, 2025
  6. ; (, Inventiones mathematicae)
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