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).
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 respeclă
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