Transverse Lusternik–Schnirelmann category of Riemannian foliations

Colman, Hellen

doi:10.1016/j.topol.2003.12.006

Cited by 5 publications

(7 citation statements)

References 8 publications

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“…The following is a direct consequence of Proposition 8.1, and generalizes the results of Colman in [15]. (M, F); hence the estimates (49) also hold for the transverse LS category.…”

Section: Foliations With Finite Categorysupporting

confidence: 74%

“…The notion of foliated homotopy extends naturally to the case of singular foliations, so that one can define the transverse category cat ∩ | (M, E) of E. We recall two topological lemmas due to Colman [15] which are used to relate the transverse categories of F and E. …”

Section: Transverse Categorymentioning

confidence: 99%

“…Also, the transverse LS category is an invariant of foliated homotopy. The transverse saturated category cat ∩ | (M, F ) has been further studied by various authors [13,14,16,36,38,43,65].…”

Section: Introductionmentioning

confidence: 99%

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Transverse LS category for Riemannian foliations

Hurder

Töben

2009

Trans. Amer. Math. Soc.

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“…The following is a direct consequence of Proposition 8.1, and generalizes the results of Colman in [15]. (M, F); hence the estimates (49) also hold for the transverse LS category.…”

Section: Foliations With Finite Categorysupporting

confidence: 74%

Section: Transverse Categorymentioning

confidence: 99%

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Transverse LS category for Riemannian foliations

Hurder

Töben

2009

Trans. Amer. Math. Soc.

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“…The transverse saturated category for Riemannian foliations of compact manifolds has been further studied by the first author [8]. The results of this paper and the structure theory for Riemannian foliations are applied to give a criterion for when cat ∩ | (M ) < ∞ for a Riemannian foliation.…”

Section: Theorem 23 ([22]) If (M F ) Is a Compact Foliation Of A Cmentioning

confidence: 99%

LS-category of compact Hausdorff foliations

Colman

Hurder

2003

Trans. Amer. Math. Soc.

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Abstract. The transverse (saturated) Lusternik-Schnirelmann category of foliations, introduced by the first author, is an invariant of foliated homotopy type with values in {1, 2, . . . , ∞}. A foliation with all leaves compact and Hausdorff leaf space M/F is called compact Hausdorff. The transverse saturated category cat ∩ | M of a compact Hausdorff foliation is always finite.In this paper we study the transverse category of compact Hausdorff foliations. Our main result provides upper and lower bounds on the transverse category cat ∩ | (M ) in terms of the geometry of F and the Epstein filtration of the exceptional set E. The exceptional set is the closed saturated foliated space which is the union of the leaves with non-trivial holonomy. We prove thatWe give examples to show that both the upper and lower bounds are realized, so the estimate is sharp. We also construct a family of examples for which the transverse category for a compact Hausdorff foliation can be arbitrarily large, though the category of the leaf spaces is constant.

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“…The transverse Lusternik-Schnirelmann category cat ∩ | (M, F ) of a foliated manifold (M, F ) was introduced in H. Colman's thesis [4,8]. This notion (and the analogous one of saturated transverse category) has been studied by several authors in the last years [5,6,14,15,17,26].…”

Section: Introductionmentioning

confidence: 99%

A cohomological lower bound for the transverse LS category of a foliated manifold

Macías–Virgós¹

2011

Illinois J. Math.

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Let F be a compact Hausdorff foliation on a compact manifold. Let E >0,• 2 = ⊕{E p,q 2 : p > 0, q ≥ 0} be the subalgebra of cohomology classes with positive transverse degree in the E 2 term of the spectral sequence of the foliation. We prove that the saturated transverse Lusternik-Schnirelmann category of F is bounded below by the length of the cup product in E >0,• 2 . Other cohomological bounds are discussed.2000 Mathematics Subject Classification. Primary 57R30, 55M30. Secondary 55T99.

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Transverse Lusternik–Schnirelmann category of Riemannian foliations

Cited by 5 publications

References 8 publications

Transverse LS category for Riemannian foliations

Transverse LS category for Riemannian foliations

LS-category of compact Hausdorff foliations

A cohomological lower bound for the transverse LS category of a foliated manifold

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