The genus and the category of configuration spaces

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.