Explicit formulae for the rational L–S category of some homogeneous spaces

Explicit formulae for rational Lusternik–Schnirelman (L–S) category (cat0) are rare, but some are available for a class of spaces which includes homogeneous spaces G/H when H is a product of at most 3 rank 1 groups, and rank G−rank Hless-than-or-equals, slant1. We extend the applicability of these formulae to the case when rank G=5 and H is a 4-torus or (SU2)4. With a Sullivan minimal model as data, implementing the formula requires the selection of a regular subsequence of length 4 from a sequence f1,…,f5 of homogeneous polynomials in 4 variables satisfyingimagedimQ[x1,…,x4]/(f1,…,f5)<∞.Such subsequences are readily obtainable, and the ease of computation is in contrast to most available methods for determining rational L–S category, which usually involve both upper and lower bounds and a good measure of luck.