11 citations · 13 across the 5 of their papers we have counts for
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Axiomatic Sectional category, Topological complexity, and Homotopic distance
Jean-Paul Doeraene, Mohammed El Haouari
Many of the properties of sectional category, topological complexity and homotopic distance are in fact derived from a small number of basic properties, which, once established, le…
About sectional category of the Ganea maps
Jean-Paul Doeraene
We first compute the James' sectional category (secat) of the Ganea map g_k of any map f in terms of the sectional category of f: We show that secat(g_k) is the integer part of sec…
Yet another Hopf Invariant
Jean-Paul Doeraene, Mohammed El Haouari
The classical Hopf invariant is defined for a map f: S^r -> X. Here we define `hcat' which is some kind of Hopf invariant built with a construction in Ganea's style, valid for maps…
Up to one approximations of sectional category and topological complexity
Jean-Paul Doeraene, Mohammed El Haouari
James' sectional category and Farber's topological complexity are studied in a general and unified framework. We introduce `relative' and `strong relative' forms of the category fo…
Ganea and Whitehead definitions for the tangential Lusternik-Schnirelmann category of foliations
Jean-Paul Doeraene, Enrique Macias-Virgós, Daniel Tanré
This work solves the problem of elaborating Ganea and Whitehead definitions for the tangential category of a foliated manifold. We develop these two notions in the category $\Tops$…