Abstract
In this chapter we start by viewing E as a principal bundle for the group Spinc(2n), which contains the unitary group. The fact that Spinc(2n) also contains the spin group Spin(2n), which is a twofold cover of SO(2n), allows us to introduce a connection in this principal bundle which has the desired compatibility with the Levi-Civita connection. Using this connection in E, we will give the definition of the spin-c Dirac operator D in (5.14). In Lemma 5.5 it is established that D is selfadjoint and has the same principal symbol as the Dolbeault-Dirac operator.
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© 1996 Birkhäuser Boston
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Duistermaat, J.J. (1996). The Spin-c Dirac Operator. In: The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator. Progress in Nonlinear Differential Equations and their Applications, vol 18. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5344-0_5
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DOI: https://doi.org/10.1007/978-1-4612-5344-0_5
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-5346-4
Online ISBN: 978-1-4612-5344-0
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