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Journal of Functional Analysis 238 (2006) 126 www.elsevier.com/locate/jfa

Summary: Journal of Functional Analysis 238 (2006) 1­26
An index theorem for Toeplitz operators on
odd-dimensional manifolds with boundary
Xianzhe Dai a,,1
, Weiping Zhang b,2
a Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
b Chern Institute of Mathematics & LPMC, Nankai University, Tianjin 300071, PR China
Received 29 April 2003; accepted 9 May 2006
Available online 27 June 2006
Communicated by Richard B. Melrose
We establish an index theorem for Toeplitz operators on odd-dimensional spin manifolds with bound-
ary. It may be thought of as an odd-dimensional analogue of the Atiyah­Patodi­Singer index theorem for
Dirac operators on manifolds with boundary. In particular, there occurs naturally an invariant of type
associated to K1 representatives on even-dimensional manifolds, which should be of independent interests.
For example, it gives an intrinsic interpretation of the so called Wess­Zumino term in the WZW theory in
© 2006 Elsevier Inc. All rights reserved.
Keywords: Toeplitz operators; Odd-dimensional manifolds; Index theorem; Eta type invariant


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics