Collected papers of Raoul Bott. Vol. 3: Foliations. Ed. by Robert D. MacPherson.

*(English)*Zbl 0820.01027
Contemporary Mathematicians. Basel: Birkhäuser. xxxi, 610 p., Set: DM 678,00; öS 5.288,40; sFr 598,00; £ 265,00 (1995).

The third volume [for Vols. 1, 2 (1994), cf. Zbl 0807.01033 and 820.01026] of Bott’s Collected Papers follows the pattern of the whole set. Covering a decade of 1970s, it is devoted to foliations. Like the preceding volumes, it starts with the Bott’s bibliography, which is followed by a few essays on Bott’s work, and then it is completed by carefully photocopied 19 Bott’s papers on the title subject (most are items 51-71 from the bibliography). The content of the volume and its appreciation are best described by Bott himself, whose personal comments on some of the papers in Volume 3 start as follows:

“Except for two purely expository reports, the papers here collected are all related to the algebraic topology aspects of foliations, the Gelfand- Fuks cohomology of vector fields and the relationships between these two at quite disparate subjects. Contemplated now in retrospect, this collection of short papers reminds one of sketches for a large canvas. Yet the canvas is missing! Even now, twenty years later, the picture is too incomplete to be painted, and the subject will – like sleeping beauty – have to await some prince of a new idea to reinvigorate it. The comments are most interesting to read, but besides them there are also personal recollections by P. Baum and two surveys by L. Conlon and A. Haefliger “who have admirably described the backdrop for these developments and the many crosscurrents in which they took place” (Bott).

Again, the volume will be indispensable in every topological library.

“Except for two purely expository reports, the papers here collected are all related to the algebraic topology aspects of foliations, the Gelfand- Fuks cohomology of vector fields and the relationships between these two at quite disparate subjects. Contemplated now in retrospect, this collection of short papers reminds one of sketches for a large canvas. Yet the canvas is missing! Even now, twenty years later, the picture is too incomplete to be painted, and the subject will – like sleeping beauty – have to await some prince of a new idea to reinvigorate it. The comments are most interesting to read, but besides them there are also personal recollections by P. Baum and two surveys by L. Conlon and A. Haefliger “who have admirably described the backdrop for these developments and the many crosscurrents in which they took place” (Bott).

Again, the volume will be indispensable in every topological library.

Reviewer: R.Duda (Wrocław)