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**Collected papers of Raoul Bott. Vol. 1: Topology and Lie groups. Ed. by Robert D. MacPherson.**
*(English)*
Zbl 0820.01026

Contemporary Mathematicians. Basel: Birkhäuser. xii, 411 p., Set: DM 678,00; öS 5.288,40; sFr 598,00; £265,00 (1994).

[For the review of Vols. 2 and 3, cf. Zbl 0807.01033 and Zbl 0820.01027).]

“The Collected Papers of Raoul Bott is being published in four volumes, each one covering roughly a decade of work, and each one centered around a different subject” (from the Preface by Editor). The first volume is devoted to Topology and Lie Groups (decade of 1950s) and consists of complete Bott’s bibliography (93 items), repeated in each subsequent volume, and two parts.

Part I, Recollections and Commentaries, contains essays on aspects of Bott’s life and work, written by him, his students and collaborators. There are three notes by Bott himself, namely a short Autobiographical Sketch, a lively recollection The Dioszeger years (1923-1929) of a particular period, and most interesting personal accounts of each individual paper reprinted in this volume, written particularly for this edition. These are followed by five essays on mathematical legacy of some of Bott’s papers reprinted in this volume and written by H. Samelson, S. Smale, W. Schmid, J. Block, and M. J. Hopkins. All they “portray Bott as a mathematician, and also record his charm, his forceful spirit, and his buoyant enthusiasm for life and mathematics” (Editor).

Part II contains Bott’s contributions from the period, namely 33 carefully photocopied papers on the title subject (items 1-32 and 50 from the bibliography), including those on his famous periodicity theorem. The volume is completed by two pictures of Bott. There is no doubt that the volume will be of immense importance for all interested in modern topology and/or Bott’s legacy.

“The Collected Papers of Raoul Bott is being published in four volumes, each one covering roughly a decade of work, and each one centered around a different subject” (from the Preface by Editor). The first volume is devoted to Topology and Lie Groups (decade of 1950s) and consists of complete Bott’s bibliography (93 items), repeated in each subsequent volume, and two parts.

Part I, Recollections and Commentaries, contains essays on aspects of Bott’s life and work, written by him, his students and collaborators. There are three notes by Bott himself, namely a short Autobiographical Sketch, a lively recollection The Dioszeger years (1923-1929) of a particular period, and most interesting personal accounts of each individual paper reprinted in this volume, written particularly for this edition. These are followed by five essays on mathematical legacy of some of Bott’s papers reprinted in this volume and written by H. Samelson, S. Smale, W. Schmid, J. Block, and M. J. Hopkins. All they “portray Bott as a mathematician, and also record his charm, his forceful spirit, and his buoyant enthusiasm for life and mathematics” (Editor).

Part II contains Bott’s contributions from the period, namely 33 carefully photocopied papers on the title subject (items 1-32 and 50 from the bibliography), including those on his famous periodicity theorem. The volume is completed by two pictures of Bott. There is no doubt that the volume will be of immense importance for all interested in modern topology and/or Bott’s legacy.

Reviewer: R.Duda (Wrocław)