## 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.

### MSC:

 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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