Norio Iwase

Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp

Japanese
Authors.
myself
Abstract.
We first introduce a homotopy-theoretical version of Fox's categorical sequence in terms of a new reltive L-S cateory, which gives a better upper estimate `the categorical length' for the L-S category than Ganea's cone length. Then we discuss how higher Hopf invariants fit with the categorical sequence through our relative L-S category. We also clarify the relations among our new relative L-S category and other three known relative L-S categories introduced by Fadell and Husseini, by Berstein and Ganea and by Arkowitz and Lupton. The main goal of this paper is to show that the categorical length is equal to the L-S category. In addition, the definition of cup length and module weight for our relative L-S category are given.

Categorical length, relative L-S category and higher Hopf invariants (adobe-pdf file, 180kb)