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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).
Table des matières
- 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.
