10 research outputs found
Ganea and Whitehead definitions for the tangential Lusternik-Schnirelmann category of foliations
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 of stratified spaces, that are topological
spaces endowed with a partition \cF and compare them to a third invariant
defined by using open sets. More precisely, these definitions apply to an
element (X,\cF) of \Tops together with a class \cA of subsets of ;
they are similar to invariants introduced by M. Clapp and D. Puppe.
If (X,\cF)\in\Tops, we define a transverse subset as a subspace of
such that the intersection is at most countable for any S\in \cF.
Then we define the Whitehead and Ganea LS-categories of the stratified space by
taking the infimum along the transverse subsets. When we have a closed
manifold, endowed with a -foliation, the three previous definitions, with
\cA the class of transverse subsets, coincide with the tangential category
and are homotopical invariants.Comment: 14 pages, 2 figure
LS-catégorie dans une catégorie à modÚles
Doctorat en Sciences mathématiques -- UCL, 199
Logique modale propositionnelle et pr dicative (s mantique de cat gories)
SIGLEBSE B224456T / UCL - Université Catholique de LouvainBEBelgiu