A notion of geometric complexity and its application to topological rigidity

Erik Guentner; Romain Tessera; Guoliang Yu

doi:10.1007/s00222-011-0366-z

A notion of geometric complexity and its application to topological rigidity

Erik Guentner
, Romain Tessera
, Guoliang Yu

University of Hawaii
Vanderbilt University
CNRS UMR 5669, 'Unité de Mathématiques Pures et Appliquées' and project-team Inria NUMED, Ecole Normale Supérieure de Lyon

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

68 Citations (Scopus)

Résumé

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then M×ℝ ⁿ is homeomorphic to N×ℝ ⁿ, for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K.

langue originale	Anglais
Pages (de - à)	315-357
Nombre de pages	43
journal	Inventiones Mathematicae
Volume	189
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s00222-011-0366-z
état	Publié - 1 août 2012
Modification externe	Oui

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AB - We introduce a geometric invariant, called finite decomposition complexity (FDC), to study topological rigidity of manifolds. We prove for instance that if the fundamental group of a compact aspherical manifold M has FDC, and if N is homotopy equivalent to M, then M×ℝ n is homeomorphic to N×ℝ n, for n large enough. This statement is known as the stable Borel conjecture. On the other hand, we show that the class of FDC groups includes all countable subgroups of GL(n,K), for any field K.

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A notion of geometric complexity and its application to topological rigidity

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