On automorphisms of high-dimensional solid tori

Bustamante, Mauricio¹ ; Randal-Williams, Oscar²

¹ Departamento de Matemáticas, Universidad Católica de Chile, Santiago, Chile
² Centre for Mathematical Sciences, University of Cambridge, Cambridge, United Kingdom

Geometry & topology, Tome 28 (2024) no. 4, pp. 1629-1692.

Résumé

We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1\times D^{2n-1}$, for $2n\ge 6$, in a range of degrees up to $n-2$. Our analysis relies on understanding the homotopy fibre of a linearisation map from the plus-construction of the classifying space of a certain space of self-embeddings of stabilisations of this manifold to a form of Hermitian $K$–theory of the integral group ring of ${\pi }_1(S^1)$. We also show that these homotopy groups vanish rationally.

Détail

DOI : 10.2140/gt.2024.28.1629

Keywords: diffeomorphisms, block diffeomorphisms, solid tori, Weiss fibre sequence, self-embeddings, surgery theory, infinite generation

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