Structures riemanniennes L^p et K-homologie
Geometric Topology
2016-09-07 v1 Differential Geometry
Abstract
We construct analytically the signature operator for a new family of topological manifolds. This family contains the quasi-conformal manifolds and the topological manifolds modeled on germs of homeomorphisms of R^n possessing a derivative which is in L^p, with p > n(n+1)/2. We obtain an unbounded Fredholm module which defines a class in the K-homology of the manifold, the Chern character of which is the Hirzebruch polynomial in the Pontrjagin classes of the manifold. This generalizes previous works of N. Teleman for Lipschitz manifolds and of A. Connes, N. Teleman and D. Sullivan for quasi-conformal manifolds of even dimension.
Cite
@article{arxiv.math/9905210,
title = {Structures riemanniennes L^p et K-homologie},
author = {Michel Hilsum},
journal= {arXiv preprint arXiv:math/9905210},
year = {2016}
}
Comments
16 pages, published version