Utilize este identificador para referenciar este registo:
https://hdl.handle.net/1822/4382
Título: | On the algebraic approximation of Lusternik-Schnirelmann category |
Autor(es): | Kahl, Thomas |
Palavras-chave: | Lusternik-Schnirelmann category Hopf algebras up to homotopy Model categories |
Data: | Jun-2003 |
Editora: | Elsevier 1 |
Revista: | Journal of Pure and Applied Algebra |
Citação: | "Journal of Pure and Applied Algebra". ISSN 0022-4049. 181:2/3 (2003) 227-277. |
Resumo(s): | Algebraic approximations have proved to be very useful in the investigation of Lusternik-Schnirelmann category. In this paper the L.-S. category and its approximations are studied from the point of view of abstract homotopy theory. We introduce three notions of L.-S. category for monoidal cofibration categories, i.e., cofibration categories with a suitably incorporated tensor product. We study the fundamental properties of the abstract invariants and discuss, in particular, their behaviour with respect to cone attachments and products. Besides the topological L.-S. category the abstract concepts cover classical algebraic approximations of the L.-S. category such as the Toomer invariant, rational category, and the A- and M-categories of Halperin and Lemaire. We also use the abstract theory to introduce a new algebraic approximation of L.-S. category. This invariant which we denote by $\ell$ is the first algebraic approximation of the L.-S. category which is not necessarily $\leq 1$ for spaces having the same Adams-Hilton model as a wedge of spheres. For a space $X$ the number $\ell (X)$ can be determined from an Anick model of $X$. Thanks to the general theory one knows \textit{a priori} that $\ell$ is a lower bound of the L.-S. category which satisfies the usual product inequality and increases by at most 1 when a cone is attached to a space. |
Tipo: | Artigo |
URI: | https://hdl.handle.net/1822/4382 |
DOI: | 10.1016/S0022-4049(02)00306-7 |
ISSN: | 0022-4049 |
Versão da editora: | http://www.elsevier.com/wps/find/journaldescription.cws_home/505614/description#description |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: | CMAT - Artigos em revistas com arbitragem / Papers in peer review journals |