Contents

Idea

A type of Dirac operator defined on manifolds equipped with Spin^c structure.

Applications

• Freed-Witten anomaly

• geometric quantization by push-forward

References

A quick statement of the definition is in

• Ulrich Krämer, ${\mathrm{Spin}}^{ℂ}$-Dirac structures and Dirac operators (2009) (pdf)

Detailed accounts include

• J. J. Duistermaat, The Spin-c Dirac Operator, in The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator Modern Birkhäuser Classics, 2011, 41-51, DOI: 10.1007/978-0-8176-8247-7_5

• Eckhard Meinrenken, Symplectic Surgery and the Spin-C Dirac operator (arXiv:dg-ga/9504002)

• Charles Epstein, Subelliptic ${\mathrm{Spin}}_{ℂ}$-Dirac operators, I (pdf)