## About the Transverse Fixed Point Formula for Foliations

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 1, Page 17--32.

Benameur, Moulay-Tahar
About the Transverse Fixed Point Formula for Foliations
Let $(V,F)$ be a compact foliated manifold and fix any Riemannian metric $g$ on $V$. Let $f$ be any isometry of $(V,g)$ which preserves the longitudinal bundle $F$ and denote by $H$ the compact Lie group of isometries generated by $f$. We give here a generalization of the Atiyah-Segal localization theorem to the space of leaves. Using the $H$-equivariant fundamental spectral triple of Connes-Moscovici, this then enables to deduce topological informations about the existence of fixed leaves under the action of a compact Lie group.
Keywords: C$^{*}$-algebras, foliations, K-theory