On some Lusternick-Schnirelmann type invariants


Abstract


In this paper, we show that the invariant \mathrm{R}_0(X), introduced in [15], coincides with cat_0(X) for any rationally elliptic space X. Additionally, we define, for any space X over an arbitrary field \mathbb{K}, an {\it Ext-version} homotpy invariant \mathrm{L}_{\mathbb{K}}(X) of the Ginsburg invariant l_{\mathbb{K}}(X). Then, we establish the equality between \mathrm{L}_{0}(X):=\mathrm{L}_{\mathbb{Q}}(X) and l_0(X) in the case where X is rationally elliptic.

Keywords: LS-category; Toomer and Ginsburg invariants; Milnor-Moore and Eilenberg-Moore spectral sequences

Full Text: PDF
کاغذ a4 ویزای استارتاپ

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.