solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看11683次
Delocalized eta invariants, cyclic cohomology and higher rho invariants. (arXiv:1901.02378v1 [math.KT])
来源于:arXiv
The first main result of this article is to prove the convergence of Lott's
delocalized eta invariant holds for all invertible operators. Our second main
result is to construct a pairing between delocalized cyclic cocycles of the
group algebra of the fundamental group of a manifold and K-theoretic higher rho
invariants of the manifold, when the fundamental group is hyperbolic. As an
application, under the assumption of hyperbolicity of the fundamental group, we
compute the delocalized part of the Connes-Chern character of
Atiyah-Patodi-Singer type K-theoretic higher indices, for example, the higher
index of a spin manifold with boundary where the boundary carries a positive
scalar curvature metric. Our explicit formula for this delocalized Connes-Chern
character is expressed in terms of our pairing of delocalized cyclic cocycles
and higher rho invariants on the boundary of manifold. 查看全文>>