2015/08/31 by Oliver Goertsches, Hiraku Nozawa, Dirk Toeben · 1 citation
Mathematics · #math.DG #msc:55N25 #msc:57R30 #msc:58J28 #msc:53D35
published as Israel J. Math. 222 (2017), no. 2, 867-920 · 36 pages
arxiv created 2015/08/31 · arxiv updated 2018/03/16
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.