Geometry & Topology

Some finiteness results for groups of automorphisms of manifolds

Alexander Kupers

Abstract

We prove that in dimension $≠4,5,7$ 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 $ℝn$ and various types of automorphisms of $2$–connected manifolds.

Article information

Source
Geom. Topol., Volume 23, Number 5 (2019), 2277-2333.

Dates
Revised: 7 November 2018
Accepted: 15 December 2018
First available in Project Euclid: 22 October 2019

https://projecteuclid.org/euclid.gt/1571709625

Digital Object Identifier
doi:10.2140/gt.2019.23.2277

Mathematical Reviews number (MathSciNet)
MR4019894

Zentralblatt MATH identifier
07121752

Keywords
diffeomorphisms embeddings

Citation

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

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