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A proof and extension of Dehn's lemma

1958
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Bulletin of the American Mathematical Society
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1. Introduction. C. D. Papakyriakopoulos [2] has recently proved Dehn's lemma [l]. His proof has the merit that the basic construction (the tower) and the crucial lemmas apply to the sphere theorem as well as Dehn's lemma. However, if one is content with Dehn's lemma the proof can be simplified. In this note we first give a simplified proof of Dehn's lemma and then prove an analogous theorem for surfaces with more than one boundary curve. By a surface of type (p } r) we mean a connected,

doi:10.1090/s0002-9904-1958-10198-6
fatcat:5udqloyvqbaf5isqk3ufkvmola