Localization of Chern-Simons type invariants of Riemannian foliations
Oliver Goertsches, Hiraku Nozawa, Dirk Toeben
TL;DR
This paper develops a localization formula for Chern-Simons invariants in Riemannian foliations, enabling the computation of geometric invariants by focusing on closed leaves, with applications to Sasakian manifolds.
Contribution
It introduces an Atiyah-Bott-Berline-Vergne type localization formula for Killing foliations in equivariant basic cohomology, specifically localizing Chern-Simons invariants.
Findings
Localization of volume of Sasakian manifolds to closed leaves
Localization of secondary characteristic classes to closed leaves
Illustrative examples demonstrating the method
Abstract
We prove an Atiyah-Bott-Berline-Vergne type localization formula for Killing foliations in the context of equivariant basic cohomology. As an application, we localize some Chern-Simons type invariants, for example the volume of Sasakian manifolds and secondary characteristic classes of Riemannian foliations, to the union of closed leaves. Various examples are given to illustrate our method.
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