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Journal of Topology Advance Access originally published online on October 25, 2007
Journal of Topology 2008 1(1):16-44; doi:10.1112/jtopol/jtm001
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© 2007 London Mathematical Society

Twisted equivariant K-theory with complex coefficients

Daniel S. Freed

Department of Mathematics, University of Texas at Austin, Austin, TX 78712 USA, dafr@math.utexas.edu

Michael J. Hopkins

Department of Mathematics, Harvard University, Cambridge, MA 02138, USA, mjh@math.harvard.edu

Constantin Teleman

School of Mathematics, The University of Edinburgh, The King's Building, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom, teleman@dpmms.cam.ac.uk

Using a global version of the equivariant Chern character, we describe the complexified twisted equivariant K-theory of a space with a compact Lie group action in terms of fixed-point data. We apply this to the case of a compact group acting on itself by conjugation and relate the result to the Verlinde algebra and to the Kac numerator at q=1. Verlinde's formula is also discussed in this context.

Received February 28, 2007.

2000 Mathematics Subject Classification 19L10, 55N15, 57T10

Daniel S. Freed and Constantin Teleman were partially supported by NSF grant DMS-0072675; Michael J. Hopkins was partially supported by NSF grant DMS-9803428.



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