Cohomological tautness of singular Riemannian foliations
For a Riemannian foliation F on a compact manifold M, J. A. Alvarez Lopez proved that the geometrical tautness of F, that is, the existence of a Riemannian metric making all the leaves minimal submanifolds of M, can be characterized by the vanishing of a basic cohomology class kappa(M) is an element...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/38599 |
| Acceso en línea: | http://hdl.handle.net/10810/38599 |
| Access Level: | acceso abierto |
| Palabra clave: | singular riemannian foliations foliations tautness vector-fields tenseness geometry orbits sets |
| Sumario: | For a Riemannian foliation F on a compact manifold M, J. A. Alvarez Lopez proved that the geometrical tautness of F, that is, the existence of a Riemannian metric making all the leaves minimal submanifolds of M, can be characterized by the vanishing of a basic cohomology class kappa(M) is an element of H-1(M/F) (the Alvarez class). In thisworkwe generalize this result to the case of a singular Riemannian foliation K on a compact manifold X. In the singular case, no bundlelikemetric on X can make all the leaves ofK minimal. In this work, we prove that the Alvarez classes of the strata can be glued in a unique global Alvarez class kappa(X) is an element of H-1(X/K). As a corollary, if X is simply connected, then the restriction of K to each stratum is geometrically taut, thus generalizing a celebrated result of E. Ghys for the regular case. |
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