noncommutative topology, noncommutative geometry
noncommutative stable homotopy theory
genus, orientation in generalized cohomology
spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
A type of Dirac operator defined on manifolds equipped with Spin^c structure.
Every almost complex manifold carries a canonical spin^c structure (as discussed there). If is a complex manifold, then under the identification
of the spinor bundle with that of holomorphic differential forms, the corresponding -Dirac operator is identified with the Dolbeault-Dirac operator
The A-hat genus for the -operator is the Todd genus (e.g. Kitada 75).
Original articles include
A quick statement of the definition is in
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 -Dirac operators, I (pdf)
Last revised on July 5, 2024 at 13:46:41. See the history of this page for a list of all contributions to it.