Riemannian \(L^p\) structures and \(K\)-homology. (Structures riemanniennes \(L^p\) et \(K\)-homologie.) (French) Zbl 0942.58016

Generalizing previous works of N. Teleman for Lipschitz manifolds and of A. Connes, N. Teleman and D. Sullivan for quasi-conformal manifolds of even dimension, the author constructs 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 \(\mathbb{R}^n\) possessing a derivative which is in \(L^p\) with \(p>{1\over 2} n(n+1)\).
So, he obtains 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.


58B34 Noncommutative geometry (à la Connes)
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
57N65 Algebraic topology of manifolds
58B15 Fredholm structures on infinite-dimensional manifolds
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