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arXiv · 1703.10448

Homotopy invariance of cohomology and signature of a riemannian foliation

Georges Habib·Ken Richardson
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Abstract

We prove that any smooth foliation that admits a Riemannian foliation structure has a well-defined basic signature, and this geometrically defined invariant is actually a foliated homotopy invariant. We also show that foliated homotopic maps between Riemannian foliations induce isomorphic maps on basic Lichnerowicz cohomology, and that the Alvarez class of a Riemannian foliation is invariant under foliated homotopy equivalence.

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Georges Habib, Ken Richardson. 2017-03-30. Homotopy invariance of cohomology and signature of a riemannian foliation. https://arxiv.org/abs/1703.10448

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