Categorical length, relative L-S category and higher Hopf invariants

Norio Iwase¹
Banach Center Publ. 85 (2009), 205-224
doi:10.4064/bc85-0-15

Abstract: 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.

MSC (2000): Primary 55M30; Secondary 55Q25.
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Faculty of Mathematics
Kyushu University
Fukuoka 810-8560, Japan