An algorithm to determine LS-category and Ginsburg invariant of any rationally elliptic space

2025/07/03 by Abassi, M. T. K., Acharqy, A., Boutahir, K. +1
#55P62 #55T20 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.02590

Abstract

Let X be a rationally elliptic space. Utilizing the Gorenstein algebra structure of X, we present three algorithms that together induce a generating class of Ext^N_(ΛV,d)(ℚ,(ΛV,d)) with N being the formal dimension of X. From these algorithms, we derive an algorithm to compute the rational Lusternik-Schnirelmann category cat₀(X). Furthermore, by applying a spectral sequence argument based on the \it Eilenberg-Moore spectral sequence, we compute the rational Ginsburg invariant l₀(X) introduced by M. Ginsburg in \citeGin.

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