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Tangential Lusternik–Schnirelmann Category of Foliations
Author(s) -
Colman Hellen,
Macias-Virgós Enrique
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003113
Subject(s) - mathematics , pure mathematics , homotopy category , foliation (geology) , homotopy , bounded function , derived category , equivariant map , hausdorff space , cohomology , invariant (physics) , integrable system , mathematical analysis , geology , geochemistry , metamorphic rock , mathematical physics , functor
A new invariant of (integrable) homotopy type for foliations is introduced: the tangential category of a foliated manifold. The classical Lusternik–Schnirelmann theory is generalized to foliations and the relations of the tangential category with other known invariants such as the fibrewise and the equivariant category are studied. Cohomological lower bounds are provided in terms of foliated cohomology. If the foliation is a product, the tangential category coincides with the ordinary category of the leaves. In general it is just bounded below. Estimates are given of the tangential category for compact‐Hausdorff foliations and suspensions. Examples show that the lower and upper bounds are realized.