#### Volume 23, issue 5 (2019)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Some finiteness results for groups of automorphisms of manifolds

### Alexander Kupers

Geometry & Topology 23 (2019) 2277–2333
##### Abstract

We prove that in dimension $\ne 4,5,7$ the homology and homotopy groups of the classifying space of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses homological stability, embedding calculus and the arithmeticity of mapping class groups. From this we deduce similar results for the homeomorphisms of ${ℝ}^{n}$ and various types of automorphisms of $2$–connected manifolds.

##### Keywords
diffeomorphisms, embeddings
Primary: 57S05
##### Publication
Received: 15 January 2017
Revised: 7 November 2018
Accepted: 15 December 2018
Published: 13 October 2019
Proposed: Yasha Eliashberg
Seconded: Peter Teichner, Benson Farb
##### Authors
 Alexander Kupers Department of Mathematics Harvard University Cambridge, MA United States