The genus and the category of configuration spaces

Abstract

In this paper configuration spaces of smooth manifolds are considered. The accent is made on actions of certain groups (mostly $p$-tori) on this spaces by permuting their points. For such spaces the cohomological index, the genus in the sense of Krasnosel'skii-Schwarz, and the equivariant Lyusternik-Schnirelmann category are estimated from below, and some corollaries for functions on configuration spaces are deduced.

References in corpus (1)

• On the category of Euclidean configuration spaces and associated fibrations

Cited by in corpus (7)

• Convex Equipartitions: The Spicy Chicken Theorem
• Equipartition of several measures
• Dwyer-Kan homotopy theory of enriched categories
• Equivariant Topology of Configuration Spaces
• Waist of the sphere for maps to manifolds
• The Schwarz genus of the Stiefel manifold and counting geometric configurations
• Configuration-like spaces and coincidences of maps on orbits