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April 2022 Baum–Connes and the Fourier–Mukai transform
Heath Emerson, Daniel Hudson
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Illinois J. Math. 66(1): 31-57 (April 2022). DOI: 10.1215/00192082-9725548

Abstract

The Fourier–Mukai transform from algebraic geometry may be formulated in KK-theory as the map of composition with a certain topological correspondence in the sense of Connes and Skandalis. The goal of this note is to analyze this correspondence and to describe the induced map in terms of certain natural Baum–Douglas cycles and cocycles for tori. This leads to a purely geometric description of the Baum–Connes assembly map for free Abelian groups.

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Heath Emerson. Daniel Hudson. "Baum–Connes and the Fourier–Mukai transform." Illinois J. Math. 66 (1) 31 - 57, April 2022. https://doi.org/10.1215/00192082-9725548

Information

Received: 23 September 2020; Revised: 27 December 2021; Published: April 2022
First available in Project Euclid: 3 February 2022

Digital Object Identifier: 10.1215/00192082-9725548

Subjects:
Primary: 46L80
Secondary: 58J20

Rights: Copyright © 2022 by the University of Illinois at Urbana–Champaign

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Vol.66 • No. 1 • April 2022
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