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Papers on Group Theory and Topology

  • Authors
  • Max Dehn

Table of contents

  1. Front Matter
    Pages i-viii
  2. Max Dehn
    Pages 1-4
  3. Max Dehn
    Pages 5-46
  4. Max Dehn
    Pages 47-51
  5. Max Dehn
    Pages 52-85
  6. Max Dehn
    Pages 86-91
  7. Max Dehn
    Pages 127-132
  8. Max Dehn
    Pages 133-178
  9. Max Dehn
    Pages 179-182
  10. Max Dehn
    Pages 200-202
  11. Max Dehn
    Pages 203-228
  12. Max Dehn
    Pages 229-233
  13. Max Dehn
    Pages 253-255
  14. Max Dehn
    Pages 256-362
  15. John Stillwell
    Pages 363-396

About this book

Introduction

The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .

Keywords

Group theory topology transformation

Bibliographic information