IJPAM: Volume 74, No. 2 (2012)

SPIN$^\mathbb{C}$ QUANTIZATION IN ODD DIMENSIONS

J. Fabian Meier
University of Bonn
Endenicher Allee, 60
53115, Bonn, GERMANY


Abstract. We define and discuss an extension of the $\Spinc$ quantization concept to odd-dimensional manifolds. After that we describe its relation to (the usual) even-dimensional $\Spinc$ quantization and how its famous properties like ``Quantization commutes with reduction'' can be regained in odd dimensions. At the end, we analyse the situation on 3-manifolds and give some examples.

Received: December 7, 2011

AMS Subject Classification: 53D50, 57S15

Key Words and Phrases: spinc quantization, Dirac operator, circle action

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 74
Issue: 2