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Book Review

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Book Information

Author(s): J. J. Duistermaat
Title: The heat kernel Lefschetz fixed point formula for the $\text {Spin}^c$ dirac operator
Additional book information: Progr. Nonlinear Differential Equations Appl., vol. 18, Birkhäuser, Basel and Boston, MA, vii+247 pp., $38.50, ISBN 0-8176-3865-2

References:

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[ABP]
M. F. Atiyah, R. Bott, V. K. Patodi, On the heat equation and the index theorem, Invent. math. 19 (1973), 279-330.MR 58:31287

[ABS]
M. F. Atiyah, R. Bott, A. A. Shapiro, Clifford modules, Topology 3 (1964), 3-38. MR 29:5250

[AS]
M. F. Atiyah, I. M. Singer, The index of elliptic operators. I, Ann. Math. 87 (1968), 484-530; III, Ann. Math. 87 (1968), 546-604; IV, Ann. Math. 93 (1971), 119-138; V, Ann. Math. 93 (1971), 139-149. MR 38:5243; MR 38:5245;MR 43:5554; MR 43:5555

[ASe]
M. F. Atiyah, G. B. Segal, The index of elliptic operators II, Ann. of Math. 87 (1968), 531-545. MR 38:5244

[BGV]
N. Berline, E. Getzler, M. Vergne, Heat kernels and Dirac operators., Springer-Verlag, Berlin, 1992. MR 94e:58130

[BV]
N. Berline, M. Vergne, A computation of the equivariant index of the Dirac operator, Bull. Soc. Math. Fr. 113 (1985), 305-345. MR 87f:58146

[D]
S. K. Donaldson, The Seiberg-Witten equations and $4$-manifold topology., Bull. Amer. Math. Soc. 33 (1996), 45-70. MR 1:339 810

[G]
E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), 111-117. MR 87h:58207

[GGK]
V. Ginzburg, V. Guillemin, Y. Karshon, Cobordism theory and localization formulas for Hamiltonian group actions, Internat. Math. Res. Notices 1996, no. 5, pp. 221-234. MR 1:383 756

[H]
F. Hirzebruch, A Riemann-Roch Theorem for differentiable manifolds, Séminaire Bourbaki (177) (1959).

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F. Hirzebruch and H. Hopf, Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten, Math. Annalen 136 (1958), 156-172. MR 20:7272

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E. Lerman, Symplectic cuts, Math. Res. Lett 2 (1995), 247-258. MR 96f:58062

[M]
E. Meinrenken, Symplectic surgery and the $\text {Spin}^c$ -Dirac operator, Adv. Math. (to appear).

[R]
J. Roe, Elliptic operators, topology and asymptotic methods, Pitman Research Notes in Mathematics Series 179, Longman Scientific & Technical, Essex, England, 1988. MR 89j:58126

[T1]
C. H. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Lett. 1 (1994), 809-822. MR 95j:57039

[T2]
-, More constraints on symplectic forms from Seiberg-Witten invariants, Math. Res. Lett. 2 (1995), 9-13. MR 96a:57075

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-, ${\text {S}W}\Rightarrow {\text {G}r}:$ from the Seiberg-Witten equations to pseudo-holomorphic curves, J. Amer. Math. Soc. 9 (1996), 845-918. MR 1:362 874

Additional Information:

Reviewer(s):
Daniel S. Freed
Affiliation: University of Texas, Austin
Email: dafr@math.utexas.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 34 (1997), 73-78.

MSC (1991): Primary 58-XX
DOI: 10.1090/S0273-0979-97-00698-8
PII: S 0273-0979(97)00698-8
Copyright of article: Copyright 1997, American Mathematical Society

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