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Hopf-Cyclic cohomology and the chern character for principal extensions of noncommutative algebras

Objectif

Noncommutative geometry grew out of a fusion of operator algebras and differential geometry. In the latter, spaces are thought of as sets of points and functions on them are auxiliary objects. Noncommutative geometry inverts this picture by placing the abs tract concept of functions at the centre of the theory and making a generalised space a derived notion. In the spirit of the Gelfand-Naimark theorem establishing the equivalence of commutative C*-algebras and locally compact Hausdorff spaces, the generali sed spaces given by noncommutative algebras are called noncommutative or quantum spaces. This opens up the world of naturally occurring examples of quantum spaces and turns out to be extremely helpful in studying some particularly difficult spaces, e.g. s paces of foliations, where standard techniques do not work. The main goal of this noncommutative geometry project is the comparison study and applications of Hopf-cyclic cohomology with general coefficients and the Chern-Galois character. These new methods should be compared and related both abstractly and in examples. They are purported to enhance the applicability of the celebrated index formula in computing invariants of K-theory. The project strategy is to continue exploiting the mutual feedback between algebra and analysis and between theory and examples. The aforementioned newly developed tools are examples of the successful implementation of this strategy during the applicant\"s Marie Curie fellowship. Broad and intensive collaboration as well as effe ctive import of expertise are very much needed to carry out this project. Therefore, taking into account that the particular structure of research financing in Poland hinders the international collaboration of Polish scientists, obtaining European funds is of great importance to achieve the successful re-integration of the applicant in his home country and improve his professional career opportunities.

Appel à propositions

FP6-2002-MOBILITY-11
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Coordinateur

MATHEMATICAL INSTITUTE OF THE POLISH ACADEMY OF SCIENCES
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Sniadeckich 8
WARSAW
Pologne

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