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This note proves that, as K-theory elements, the symbol classes of the de Rham operator and the signature operator on a closed manifold of even dimension are congruent mod 2. An equivariant generalization is given pertaining to the equivariant Euler characteristic and the multi-signature.
This paper deals with two aspects of the theory of characteristic classes of star products: first, on an arbitrary Poisson manifold, we describe Morita equivalent star products in terms of their Kontsevich classes; second, on symplectic manifolds, we
Let $C$ be a unital AH-algebra and $A$ be a unital simple C*-algebra with tracial rank zero. It has been shown that two unital monomorphisms $phi, psi: Cto A$ are approximately unitarily equivalent if and only if $$ [phi]=[psi] {rm in} KL(C,A) and ta
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein m
Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg trace formula is an equality arising from computing in two different ways the traces of convolution operators on the Hilbert space L^2(G/H) associated to test functions. In t
We present three new inequalities tying the signature, the simplicial volume and the Euler characteristic of surface bundles over surfaces. Two of them are true for any surface bundle, while the third holds on a specific family of surface bundles, na