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CONFIGURATION CATEGORIES AND HOMOTOPY AUTOMORPHISMS

Part of: Differential topology Homotopy theory

Published online by Cambridge University Press:  19 November 2018

MICHAEL S. WEISS
MICHAEL S. WEISS*
Affiliation:
Math. Institut, Universität Münster, 48149 Münster, Einsteinstrasse 62, Germany E-mail: [email protected]
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Abstract

Let M be a smooth compact manifold with boundary. Under some geometric conditions on M, a homotopical model for the pair (M, ∂M) can be recovered from the configuration category of M \ ∂M. The grouplike monoid of derived homotopy automorphisms of the configuration category of M \ ∂M then acts on the homotopical model of (M, ∂M). That action is compatible with a better known homotopical action of the homeomorphism group of M \ ∂M on (M, ∂M).

MSC classification

Primary: 57R19: Algebraic topology on manifolds
Secondary: 55P65: Homotopy functors
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 1 , January 2020 , pp. 13 - 41
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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