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- W4297734603 abstract "Let $X$ be a finite type simply connected rationally elliptic CW-complex with Sullivan minimal model $(Lambda V, d)$ and let $kgeq 2$ the biggest integer such that $d=sum_{igeq k}d_i$ with $d_i(V)subseteq Lambda ^iV$. We show that: $cat(X_{mathbb{Q}}) = depht(Lambda V, d_k)$ if and only if $(Lambda V,d_{k})$ is elliptic. This result is obtained by introducing tow new spectral sequences that generalize the Milnor-Moore spectral sequence and its $mathcal{E}xt$-version cite{Mur94}. As a corollary, we recover a known result proved - with different methods - by L. Lechuga and A. Murillo in cite{LM02} and G. Lupton in cite{Lup02}: If $(Lambda V,d_{k})$ is elliptic, then $cat(X_{mathbb{Q}}) = dim(pi_{odd}(X)otimesmathbb{Q}) + (k-2)dim(pi_{even}(X)otimesmathbb{Q})$. In the case of a field ${IK}$ of $char({IK})=p$ (an odd prim) we obtain an algebraic approach for $e_{IK}(X)$ where $X$ is an $r$-connected ($rgeq 1$) finite CW-complex such that $p> dim(X)/r$." @default.
- W4297734603 created "2022-09-30" @default.
- W4297734603 creator A5046683626 @default.
- W4297734603 date "2009-10-25" @default.
- W4297734603 modified "2023-10-09" @default.
- W4297734603 title "LS-Category and the Depth of Rationally Elliptic Spaces" @default.
- W4297734603 doi "https://doi.org/10.48550/arxiv.0910.4660" @default.
- W4297734603 hasPublicationYear "2009" @default.
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