Geometry & Topology
- Geom. Topol.
- Volume 23, Number 5 (2019), 2277-2333.
Some finiteness results for groups of automorphisms of manifolds
We prove that in dimension 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 and various types of automorphisms of –connected manifolds.
Geom. Topol., Volume 23, Number 5 (2019), 2277-2333.
Received: 15 January 2017
Revised: 7 November 2018
Accepted: 15 December 2018
First available in Project Euclid: 22 October 2019
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Kupers, Alexander. Some finiteness results for groups of automorphisms of manifolds. Geom. Topol. 23 (2019), no. 5, 2277--2333. doi:10.2140/gt.2019.23.2277. https://projecteuclid.org/euclid.gt/1571709625