Equivariant parametrized topological complexity

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 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.

arXiv comment21 pages. The paper has been accepted for the publication in the journal Proceedings of the Royal Society of Edinburgh Section A

References in corpus (7)

• Higher topological complexity and its symmetrization
• Equivariant topological complexity
• Topology of parametrised motion planning algorithms
• Projective product spaces
• Obstructions for constructing equivariant fibrations
• Sequential parametrized topological complexity and related invariants
• Equivariant parametrized topological complexity

Cited by in corpus (1)

• Equivariant parametrized topological complexity