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Ls category, foliated spaces and transverse invariant measure
- Autor/a
- Meniño Cotón, Carlos
The LS category is a homotopy invariant given by the minimum of open
subsets, contractible within a topological space, needed to cover it.
It was introduced by Lusternik and Schnirelmann in 1934 in the setting
of variational calculus. Many variants of this notion has been given.
In particular, E. Macías and H. Colman introduced a tangential
version for foliations, where they used leafwise contractions to
transversals. In this work, we introduce and study several new
versions of the tangential LS category. The first two of them, called
measurable category and measurable _-category, are defined for
measurable laminations, which are laminations where the ambient
topology is removed and only the leaf topology and ambient measurable
structure remain; thus we use tangential deformations of open sets to
transversals that are leafwise continuous and measurable on the
ambient space.
Data sheet
- Edition
- 1
- Publication place
- Santiago de Compostela
- Editorial
- Universidade de Santiago de Compostela. Servizo de Publicacións e Intercambio Científico
- Publication Year
- 12/02/2012
- File Size
- 1.3 MB
- Serie
- Publicaciones del Departamento de Geometría y Topología
- ISBN
- 9788489390393
- Availability
- Si
The LS category is a homotopy invariant given by the minimum of open
subsets, contractible within a topological space, needed to cover it.
It was introduced by Lusternik and Schnirelmann in 1934 in the setting
of variational calculus. Many variants of this notion has been given.
In particular, E. Macías and H. Colman introduced a tangential
version for foliations, where they used leafwise contractions to
transversals. In this work, we introduce and study several new
versions of the tangential LS category. The first two of them, called
measurable category and measurable _-category, are defined for
measurable laminations, which are laminations where the ambient
topology is removed and only the leaf topology and ambient measurable
structure r...