Papers on Group Theory and Topology

1. Front Matter

   Pages i-viii

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2. Translator’s Introduction

   • Max Dehn

   Pages 1-4

3. Lectures on Group Theory

   • Max Dehn

   Pages 5-46

4. Translator’s Introduction 2

   • Max Dehn

   Pages 47-51

5. Lectures on Surface Topology

   • Max Dehn

   Pages 52-85

6. Translator’s Introduction 3

   • Max Dehn

   Pages 86-91

7. On the Topology of Three-Dimensional Space

   • Max Dehn

   Pages 92-126

8. Translator’s Introduction 4

   • Max Dehn

   Pages 127-132

9. On Infinite Discontinuous Groups

   • Max Dehn

   Pages 133-178

10. Translator’s Introduction 5

    • Max Dehn

    Pages 179-182

11. Transformation of Curves on Two-Sided Surfaces

    • Max Dehn

    Pages 183-199

12. Translator’s Introduction 6

    • Max Dehn

    Pages 200-202

13. The Two Trefoil Knots

    • Max Dehn

    Pages 203-228

14. Translator’s Introduction 7

    • Max Dehn

    Pages 229-233

15. On Curve Systems on Two-Sided Surfaces, with Application to the Mapping Problem

    • Max Dehn

    Pages 234-252

16. Translator’s Introduction 8

    • Max Dehn

    Pages 253-255

17. The Group of Mapping Classes

    • Max Dehn

    Pages 256-362

18. Appendix: The Dehn-Nielsen Theorem

    • John Stillwell

    Pages 363-396

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English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere.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) .

• Group theory
• topology
• transformation