Some finiteness results for groups of automorphisms of manifolds

Kupers, Alexander¹

¹ Department of Mathematics, Harvard University, Cambridge, MA, United States

Geometry & topology, Tome 23 (2019) no. 5, pp. 2277-2333.

Résumé

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.

Détail

DOI : 10.2140/gt.2019.23.2277

Classification : 57S05
Keywords: diffeomorphisms, embeddings

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