arXiv subjects

Y. Rami

Publications and source records attributed to Y. Rami.

3 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}.

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arXiv2016

On Spaces of Topological Complexity Two

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

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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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