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Translator’s Introduction 3

In: Papers on Group Theory and Topology

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  • Max Dehn

Abstract

In his first major publication in topology, Dehn uses his experience in surface topology and group theory to formulate and attack the major problems of 3-dimensional topology. Together with Poincaré [1904], the paper which follows is the foundation for almost all subsequent work in this field. A brief summary of the contents will support this claim: statement of the word and conjugacy problems for finitely presented groups, realisation of such groups as fundamental groups of surface complexes, Dehn’s lemma, the diagram of the trefoil knot group, equivalence between triviality of a knot and commutativity of its group, construction of homology spheres by surgery, and proof that one of them (actually Poincaré’s homology sphere) has finite fundamental group; all making their first appearance in print.

Suggested Citation

  • Max Dehn, 1987. "Translator’s Introduction 3," Springer Books, in: Papers on Group Theory and Topology, pages 86-91, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-4668-8_5
    DOI: 10.1007/978-1-4612-4668-8_5
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