Characteristic classes for flat Diff(M)-foliations

Autor:	Hurder, Steven
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Topology 57R20 57R32 57R50 58D05
Druh dokumentu:	Working Paper
Popis:	In this work we relate the known results about the homotopy type of classifying spaces for smooth foliations, with the homology and cohomology of the discrete group of diffeomorphisms of a smooth compact connected oriented manifold. The Mather-Thurston Theorem forms a bridge between the results on the homotopy types of classifying spaces and the various homology and cohomology groups that are studied. We introduce the algebraic K-theory of a manifold M that is derived from the discrete group of diffeomorphisms of M, and observe that the calculations of homotopy groups in this work are about these K-theory groups. We include a variety of remarks and open problems related to the study of the diffeomorphism groups and their homological invariants using the Mather-Thurston Theorem.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.09160 Zobrazit plný text záznamu View this record from Arxiv