By J.J. Duistermaat

ISBN-10: 0817682465

ISBN-13: 9780817682460

Reprinted because it initially seemed within the 1990s, this paintings is as an inexpensive text that can be of curiosity to various researchers in geometric research and mathematical physics. The book covers a variety of options primary to the learn and purposes of the spin-c Dirac operator, applying the warmth kernels conception of Berline, Getzlet, and Vergne. real to the precision and readability for which J.J. Duistermaat was once so renowned, the exposition is sublime and concise.

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Reprinted because it initially seemed within the 1990s, this paintings is as a reasonable text that should be of curiosity to a number researchers in geometric research and mathematical physics. The book covers a variety of suggestions basic to the learn and functions of the spin-c Dirac operator, using the warmth kernels conception of Berline, Getzlet, and Vergne.

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**Extra resources for The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator **

**Example text**

4) More precisely, C(V) is defined as the quotient of the tensor algebra Q9 V of V (with unit) by the two-sided ideal I, generated by the set of the elements v 0 v + Q (v, v), with v E V. 4) is equivalent to v·w+w·v==-2Q(v,w), v,wEV. 5) If one works over the complex numbers, then the rank of Q determines the Clifford algebras up to isomorphism, whereas in the real case the signature also matters. We will follow the original convention of Clifford [17] (whose point is that V can have any dimension) and take Q to be positive definite.

21), respectively.

J~ - J~ . 1) that r'(a) : ( ~ 2 [Q (~, () J~ - Q (J~, () ~] Chapter 4. The Spin Group and the Spin-c Group 38 belongs to the Lie algebra u(V) of U (V). Running through the various identifications, we see that c (a) == A' (T' (a)) . 5) We also get that T'(a), considered as a complex linear transformation in V, has complex trace equal to 2i Q(~, ~). Therefore a - ~ tracec T'(a) == a ~ i Q (~, ~) == ~ · J~ E spin(V). 7) == iRis the Lie algebra of U(l), the unit circle in C, viewed as a subset of C(V) 0 C.

### The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator by J.J. Duistermaat

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