Point-pushing actions for manifolds with boundary
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Authors
Tillmann, Ulrike
Palmer, Martin
Journal Title
Groups, Geometry, and Dynamics
ISSN
1661-7207
Publisher
European Mathematical Society
Type
Article
This Version
AM
Metadata
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Tillmann, U., & Palmer, M. Point-pushing actions for manifolds with boundary. Groups, Geometry, and Dynamics https://doi.org/10.17863/CAM.82076
Abstract
Given a manifold M and a point in its interior, the point-pushing map describes a dif- feomorphism that pushes the point along a closed path. This defines a homomorphism from the fundamental group of M to the group of isotopy classes of diffeomorphisms of M that fix the basepoint. This map is well-studied in dimension d = 2 and is part of the Birman exact sequence. Here we study, for any d 3 and k 1, the map from the k-th braid group of M to the group of homotopy classes of homotopy equivalences of the k-punctured manifold M z, and analyse its injectivity. Equivalently, we describe the monodromy of the universal bundle that associates to a configuration z of size k in M its complement, the space M z. Furthermore, motivated by our work in [PT21], we describe the action of the braid group of M on the fibres of configuration-mapping spaces.
Embargo Lift Date
2025-03-03
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.82076
This record's URL: https://www.repository.cam.ac.uk/handle/1810/334658
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