Nicolae Teleman

The index of signature operators on Lipschitz manifolds

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Characteristic classes of piecewise differentiable affine connections on smooth manifolds

Abstract We show that the Chern-Weil construction can still be used to extract the characteristic classes of smooth manifolds even from (discontinuous) piecewise differentiable Riemannian metrics and affine connections.

Almost flat bundles and almost flat structures

In this paper we discuss some geometric aspects concerning almost flat bundles, notion introduced by Connes, Gromov and Moscovici [ Conjecture de Novikov et fibres presque plats , C. R. Acad. Sci. Paris Ser. I 310 (1990), 273–277]. Using a natural construction of [B. Hanke and T. Schick, Enlargeability and index theory , preprint, 2004], we present here a simple description of such bundles. For this we modify the notion of almost flat structure on bundles over smooth manifolds and extend this notion to bundles over arbitrary CW-spaces using quasi-connections [N. Teleman, Distance function, Linear quasi-connections and Chern character , IHES/M/04/27]. Connes, Gromov and Moscovici [ Conjecture de Novikov et fibres presque plats , C. R. Acad. Sci. Paris Ser. I 310 (1990), 273–277] showed that for any almost flat bundle

Construction of Fredholm Representations and a Modification of the Higson-Roe Corona

\alpha

Modified Hochschild and Periodic Cyclic Homology

over the manifold

The algebra of piecewise differentiable currents on smooth manifolds

M

Characteristic classes of fiber bundle with involution

, the index of the signature operator with values in

Spaces of germs and jets

\alpha

The index theorem for topological manifolds

is a homotopy equivalence invariant of

Combinatorial hodge theory and signature operator

M