Thurston’s fragmentation and c-principles

Abstract In this paper, we generalize the original idea of Thurston for so-called Mather-Thurston’s theorem foliated bundles to prove new variants PL homeomorphisms and contactormorphisms. These versions answer questions posed by Gelfand-Fuks ([GF73, Section 5]) Greenberg ([Gre92]) on foliations Rybicki ([Ryb10, 11]) contactomorphisms. The interesting point about Thurston’s technique compared better-known Segal-McDuff’s proof Mather-Thurston is that it gives a compactly supported c-principle without knowing relevant local statement open balls. appendix, show fragmentation implies non-abelian Poincare duality its generalization using blob complexes ([MW12, Theorem 7.3.1]). To memory John Mather.