Raoul Bott: Collected Papers
Volume 2: Differential Operators
Published on 14. February 2012
Book
Paperback/Softback
844 pages
978-1-4612-5369-3 (ISBN)
Description
These are the terse notes for a graduate seminar which I conducted at Harvard during the Fall of 1963. By and large my audience was acquainted with the standard material in bundle theory and algebraic topology and I therefore set out directly to develop the theory of characteristic classes in both the standard cohomology theory and K-theory. Since 1963 great strides have been made in the study of K(X), notably by Adams in a series of papers in Topology. Several more modern accounts of the subject are available. In particular the notes of Atiyah, IINotes on K-theoryll not only start more elementarily, but also carry the reader further in many respects. On the other hand, those notes deal only with K-theory and not with the characteristic vii 406 viii classes in the standard cohomology. The main novelty of these lectures is really the systematic use of induced representation theory and the resulting formulae for the KO-theory of sphere bundles. Also my point of view toward the J -invariant, e(E) is slightly different from that of Adams. I frankly like my groups H\ Z+; KO(X)) and there is some indication that the recent work of Sullivan will bring them into their own.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1994
Language
English
Place of publication
Boston
United States
Target group
Professional and scholarly
Research
Illustrations
844 p.
Dimensions
Height: 26 cm
Width: 19.3 cm
Weight
1749 gr
ISBN-13
978-1-4612-5369-3 (9781461253693)
DOI
10.1007/978-1-4612-5367-9
Schweitzer Classification
Other editions
Additional editions
Book
07/1994
Birkhauser Boston Inc
€213.99
Shipment within 15-20 days
Content
- Volume 2.- The Papers of Raoul Bott.- [33] Clifford Modules.- [34] The Index Problem for Manifolds with Boundary.- [35] On the Periodicity Theorem for Complex Vector Bundles.- [36] Notes on the Lefschetz Fixed Point Theorem for Elliptic Complexes.- [37] The Index Theorem for Homogeneous Differential Operators.- [38] Hermitian Vector Bundles and the Equidistribution of the Zeroes of their Holomorphic Sections.- [39] A Fixed Point Theorem for Elliptic Complexes.- [40] A Lefschetz Fixed Point Formula for Elliptic Differential Operators.- [41] Vector Fields and Characteristic Numbers.- [42] A Lefschetz fixed point formula for elliptic complexes: I.- [43] A Residue Formula for Holomorphic Vector-Fields.- [44] A Lefschetz fixed point formula for elliptic complexes: II. Applications.- [45] Topics in Topology and Differential Geometry.- [46] Lectures on K(X).- [47] acunas for Hyperbolic Differential Operators with Constant Coefficients I.- [48] Some Formulas Related to Complex Transgression.- [49] On the Zeroes of Meromorphic Vector-Fields.- [58] On the Heat Equation and the Index Theorem.- [58a] Errata to the paper On the Heat Equation and the Index Theorem.- [62] Lacunas for Hyperbolic Differential Operators with Constant Coefficients. II.- [90] The Topological Constraints on Analysis.- Permissions - Volume 2.