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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 Hardback – iul 1994
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: 9780817636463
ISBN-10: 0817636463
Pagini: 844
Ilustrații: 844 p.
Dimensiuni: 178 x 254 x 44 mm
Greutate: 1.67 kg
Ediția:1994
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Contemporary Mathematicians

Locul publicării:Boston, MA, United States

Public țintă

Research

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.

Descriere

Descriere de la o altă ediție sau format:
This paper is a greatly expanded account of the preliminary material that appeared in Atiyah & Bott (1980). Part ofthe reason for the long delay between that paper and this present version was that new view-points emerged that added further interest to the topic and enabled us to provide proofs for what had earlier been conjectures. The length of this paper is due to our desire to present the several different aspects of the problem. We feel that this is justified because the main interest lies not so much in the actual applications as in the methods employed and the interaction between different approaches. Because ofits long gestation period and its consequent size, we feel that we owe the reader a substantial and leisurely introduction that puts the paper into historical perspective. In fact, on a personal level, one of the attractions of this subject to us is that it brings together algebraic vector bundles and Morse theory, topics to which we separately made contributions a quarter of a century ago (Atiyah 1955, 1957; Bott 1958, Bott &Samelson 1958). Even better, the catalyst that produced this interaction came from a quite unexpected quarter, namely that of theoretical physics in the form of the Yang-Mills equations.

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