In this paper we introduce the categorical length, a homotopy version of Fox categorical sequence, and an extended version of relative L-S category which contains the classical notions of Berstein-Ganea and Fadell-Husseini. We then show that, for a space or a pair, the categorical length for categorical sequences is precisely the L-S category or the relative L-S category in the sense of Fadell-Husseini respectively. Higher Hopf invariants, cup length, module weights, and recent computations by Kono and the author are also studied within this unified L-S theory based on the categorical length of categorical sequences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-15, author = {Norio Iwase}, title = {Categorical length, relative L-S category and higher Hopf invariants}, journal = {Banach Center Publications}, volume = {86}, year = {2009}, pages = {205-224}, zbl = {1170.55001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-15} }
Norio Iwase. Categorical length, relative L-S category and higher Hopf invariants. Banach Center Publications, Tome 86 (2009) pp. 205-224. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc85-0-15/