The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator
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Beschreibung
Interest in the spin-c Dirac operator originally came about from the study of complex analytic manifolds, where in the non-Kähler case the Dolbeault operator is no longer suitable for getting local formulas for the Riemann–Roch number or the holomorphic Lefschetz number. However, every symplectic manifold (phase space in classical mechanics) also carries an almost complex structure and hence a corresponding spin-c Dirac operator. Using the heat kernels theory of Berline, Getzler, and Vergne, this work revisits some fundamental concepts of the theory, and presents the application to symplectic geometry.J.J. Duistermaat was well known for his beautiful and concise expositions of seemingly familiar concepts, and this classic study is certainly no exception. Reprinted as it was originally published, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics.Overall this is a carefully written, highly readable book on a very beautiful subject. —Mathematical ReviewsThe book of J.J. Duistermaat is a nice introduction to analysis related [to the] spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. —EMS NewsletterThe author's book is a marvelous introduction to [these] objects and theories. —Zentralblatt MATH
Reprinted as it originally appeared in the 1990s, this work is as an affordable text that will be of interest to a range of researchers in geometric analysis and mathematical physics. The book covers a variety of concepts fundamental to the study and applications of the spin-c Dirac operator, making use of the heat kernels theory of Berline, Getzlet, and Vergne. True to the precision and clarity for which J.J. Duistermaat was so well known, the exposition is elegant and concise.
Affordable softcover edition of the only book ever published on the subject Written by one of the leading geometric analysts of the late 20th century Presents interesting applications of theory Gives an accessible approach to the field Includes supplementary material: sn.pub/extras
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J.J. Duistermaat
Themen in »The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator«
Dirac operator Laplace operator Lefschetz fixed point formula differential topology heat kernels spin-c group symplectic geometry partial differential equations
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Overall this is a carefully written, highly readable book on a very beautiful subject. —Mathematical Reviews
The book of J.J. Duistermaat is a nice introduction to analysis related [to the] spin-c Dirac operator. ... The book is almost self contained, [is] readable, and will be useful for anybody who is interested in the topic. —EMS Newsletter
The author's book is a marvelous introduction to [these] objects and theories. —Zentralblatt MATH
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