An algorithm to determine LS-category and Ginsburg invariant of any rationally elliptic space
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911036733390848 |
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| author | Abassi, M. T. K. Acharqy, A. Boutahir, K. Rami, Y. |
| author_facet | Abassi, M. T. K. Acharqy, A. Boutahir, K. Rami, Y. |
| contents | 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 $Ext^N_{(ΛV,d)}(\mathbb{Q},(ΛV,d))$ with $N$ being the formal dimension of $X$. From these algorithms, we derive an algorithm to compute the rational Lusternik-Schnirelmann category $cat_0(X)$. 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algorithm to determine LS-category and Ginsburg invariant of any rationally elliptic space Abassi, M. T. K. Acharqy, A. Boutahir, K. Rami, Y. Algebraic Topology 55P62, 55T20 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 $Ext^N_{(ΛV,d)}(\mathbb{Q},(ΛV,d))$ with $N$ being the formal dimension of $X$. From these algorithms, we derive an algorithm to compute the rational Lusternik-Schnirelmann category $cat_0(X)$. 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}. |
| title | An algorithm to determine LS-category and Ginsburg invariant of any rationally elliptic space |
| topic | Algebraic Topology 55P62, 55T20 |
| url | https://arxiv.org/abs/2507.02590 |