Equivariant parametrized topological complexity
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915034963116032 |
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| author | Daundkar, Navnath |
| author_facet | Daundkar, Navnath |
| contents | 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 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 sequential equivariant parametrized topological complexity of equivariant Fadell-Neuwirth fibrations and some equivariant fibrations involving generalized projective product spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant parametrized topological complexity Daundkar, Navnath Algebraic Topology 55M30, 55S40, 55R10, 55P20 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 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 sequential equivariant parametrized topological complexity of equivariant Fadell-Neuwirth fibrations and some equivariant fibrations involving generalized projective product spaces. |
| title | Equivariant parametrized topological complexity |
| topic | Algebraic Topology 55M30, 55S40, 55R10, 55P20 |
| url | https://arxiv.org/abs/2405.20809 |