Structures riemanniennes $L^p$ et $K$-homologie. (Riemannian $L^p$ structures and $K$-homology)

Michel Hilsum

Review from Zentralblatt MATH:

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 $\bbfR^n$ 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.

Reviewed by Corina Mohorianu

Keywords: $K$-homology of a manifold; Pontrjagin class; Chern character; quasi-conformal manifolds; topological manifolds

Classification (MSC2000): 58B34 58B20 57N65 58B15

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