arXiv subjects

K. Boutahir

Publications and source records attributed to K. Boutahir.

2 recordsLinked to original sources

arXiv2025

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

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 $Ext^N_{(\Lambda V,d)}(\mathbb{Q},(\Lambda V,d))$ with $N$ being the formal dimension of $X$. From these algorithms, we derive an algorithm to compute the rational Lusternik-Schnirelmann category $cat_0(X)$. Furthermore, by applying a spectral sequence argument based on the {\it Eilenberg-Moore spectral sequence}, we compute the rational Ginsburg invariant $l_0(X)$ introduced by M. Ginsburg in \cite{Gin}.

math.AT↗

arXiv2013

On L.S.-category of a family of rational elliptic spaces

Let X be a finite type simply connected rationally elliptic CW-complex with Sullivan minimal model $(ΛV, d)$ and let $k \geq 2$ the biggest integer such that $d=\sum \limits_{\underset{}{i\geq k}}d_i$ with $d_i(V) \subseteq Λ^iV$. In \cite{murillo02} the authors showed that if $(ΛV,d_k)$ is morever elliptic then $cat(ΛV,d)=(k-2)dimV^{even} + dimV^{odd}.$ Our work focuses on the estimation of L.S.-category of such spaces in the case when $k=3$ and when $(ΛV,d_3)$ is not necessarily elliptic.

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