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Raoul Bott: Collected Papers: Volume 2: Differential Operators de Robert D. MacPherson

Raoul Bott: Collected Papers: Volume 2: Differential Operators: Contemporary Mathematicians

Editat de Robert D. MacPherson
en Limba Engleză Paperback – 14 feb 2012
The Collected Papers of Raoul Bott are contained in five volumes, with each volume covering a different subject and each representing approximately a decade of Bott's work. The volumes are:

Volume 1: Topology and Lie Groups (1950's)

Volume 2: Differential Operators (1960's)

Volume 3: Foliations (1970's)

Volume 4: Mathematics Related to Physics (1980's)

Volume 5: Completive Articles and Additional Biographic Material (1990's)


This volume contains most of Raoul Bott's papers on the relations between topology and analysis. In the early 1960's, Bott, along with Atiyah, Hirzebruch, and Singer, brought about a revolution in this subject. It was an important development for twentieth century mathematics relying extensively on K-theory, as developed by Atiyah and Hirzebruch following the lead of Grothendieck in algebraic geometry, which in turn, depended on Bott's Periodicity Theorem (originally proved in Volume 1, and reproved in papers [33] and [35] of this volume).
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Specificații

ISBN-13: 9781461253693
ISBN-10: 1461253691
Pagini: 844
Dimensiuni: 193 x 260 x 44 mm
Greutate: 1.75 kg
Ediția:Softcover reprint of the original 1st ed. 1994
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Contemporary Mathematicians

Locul publicării:Boston, MA, United States

Public țintă

Research

Descriere

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.

Cuprins

— 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.

Recenzii

  "There is no doubt that the volume will be of immense importance for all interested in modern topology and/or Bott's legacy." 
  -- Zentralblatt für Mathematik (Review of Vol. 1)   
  "Each reader will certainly profit from Bott's elegant style and engagement with the central problems of the subject and time." 
  -- Mathematical Reviews (review of Vol. 1)   
  "The volume (along with the three other volumes) is highly recommended to any mathematical library, institutional as well as individual..."
  -- Mathematical Reviews (Review of Vol. 2)   
  "The volume will be indispensible in every topological library." 
  -- Zentralblatt für Mathematik (Review of Vol. 3)   

Notă biografică