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Algebra Seminar

Paschke Categories, K-homology and the Riemann-Roch Transformation

Khashayar Sartipi UIUC

Location:  Room 005
Date & time: Wednesday, 30 January 2019 at 2:00PM - 3:00PM

ABSTRACT:  For a separable C*-algebra A, we introduce an exact C*-category called the Paschke Category of A, which is completely functorial in A, and show that its K-theory groups are isomorphic to the topological K-homology groups of the C*-algebra A. Then we use the Dolbeault complex and ideas from the classical methods in Kasparov K-theory to construct an acyclic chain complex in this category, which in turn, induces a Riemann-Roch transformation in the homotopy category of spectra, from the algebraic K-theory spectrum of a complex manifold X, to its topological K-homology spectrum.

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