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Equivariant parametrized topological complexity

Part of: Classical Topics in Algebraic Topology Operations and obstructions Fiber spaces and bundles

Published online by Cambridge University Press:  26 November 2024

Navnath Daundkar
Navnath Daundkar*
Affiliation:
Department of Mathematics, Indian Institute of Science Education and Research, Pune, India ([email protected])
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Abstract

In this paper, we define and study an equivariant analogue of Cohen, Farber and Weinberger’s parametrized topological complexity. We show that several results in the non-equivariant case can be extended to the equivariant case. For example, we establish the fibrewise equivariant homotopy invariance of the sequential equivariant parametrized topological complexity. We obtain several bounds on sequential equivariant topological complexity involving the equivariant category. We also obtain the cohomological lower bound and the dimension-connectivity upper bound on the sequential equivariant parametrized topological complexity. In the end, we use these results to compute the sequential equivariant parametrized topological complexity of equivariant Fadell–Neuwirth fibrations and some equivariant fibrations involving generalized projective product spaces.

Keywords

equivariant sectional categoryparametrized topological complexityequivariant topological complexityMotion planning algorithmFadell-Neuwirth fibrationsequivariant fibrations

MSC classification

Primary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Secondary: 55S40: Sectioning fiber spaces and bundles 55R10: Fiber bundles 55R91: Equivariant fiber spaces and bundles
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 24
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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