Measure preserving pseudo-groups and a theorem of Sacksteder

Plante, J. F.

doi:10.5802/aif.550

Cited by 22 publications

(9 citation statements)

References 5 publications

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“…Cutting along the transverse torus yields a foliation of T 2 x [0, 1] which is transverse to the boundary. According to [11] this foliation has trivial holonomy so the main theorem of [20] says that the foliation on T 2 x [0, 1] may be isotoped to the foliation obtained from a foliation of the torus by parallel lines taking as leaves the surfaces (leaf in T 2) x [0, 1]. This completes the proof of (4.1).…”

Section: Folations Without Reeb Componentssupporting

confidence: 53%

Foliations of 3-manifolds with solvable fundamental group

Plante

1979

Invent Math

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Section: Folations Without Reeb Componentssupporting

confidence: 53%

Foliations of 3-manifolds with solvable fundamental group

Plante

1979

Invent Math

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“…The definitions above are all standard and well-known. We now come to the key new definition of this paper which was suggested by [4] and classical pseudogroup theory [23]. Let S be a Boolean semigroup.…”

Section: Introductionmentioning

confidence: 99%

Invariant means on Boolean inverse monoids

Kudryavtseva¹,

Lawson

Lenz

et al. 2015

Semigroup Forum

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Abstract. The classical theory of invariant means, which plays an important rôle in the theory of paradoxical decompositions, is based upon what are usually termed 'pseudogroups'. Such pseudogroups are in fact concrete examples of the Boolean inverse monoids which give rise toétale topological groupoids under non-commutative Stone duality. We accordingly initiate the theory of invariant means on arbitrary Boolean inverse monoids. Our main theorem is a characterization of when a Boolean inverse monoid admits an invariant mean. This generalizes the classical Tarski alternative proved, for example, by de la Harpe and Skandalis, but using different methods.

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“…In particular, all the leaves of ĥ ave non-exponential growth. Hence either ^ has a compact leaf or elsê is without holonomy [15]. If ^ has a compact leaf, then M fibers over S 1 [10].…”

Section: Let Lejt" 1^) Then L Is a Complete Riemannian Manifold Andmentioning

confidence: 99%