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Equivariant basic cohomology of singular Riemannian foliations

Francisco C. Caramello Jr
Sep 2022
摘要
We introduce the notion of equivariant basic cohomology of singularRiemannian foliations, and prove some elementary properties such as itsinvariance under homotopies. For the particular case of singular Killingfoliations we prove that, modulo torsion, this invariant localizes to the setof closed leaves of the foliation, in the spirit of the classical localizationtheorem of Borel. As an application, it follows that the basic Eulercharacteristic also localizes to this set.
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