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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The conjugacy problem for boundary loops in $3$-manifolds
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by Benny D. Evans PDF
Trans. Amer. Math. Soc. 240 (1978), 53-64 Request permission


A geometric solution of the word problem for fundamental groups of compact, orientable, irreducible, sufficiently large 3-manifolds has been given by F. Waldhausen. We present here a solution of a restricted version of the conjugacy problem for this same class of 3-manifolds; however, the conjugacy problem for 3-manifolds remains in general unsolved. The main results is that there is an algorithm that will determine for any two loops ${L_1},{L_2}$ in the boundary of a compact, orientable, irreducible sufficiently large 3-manifold M if ${L_1}$, is freely homotopic in M to ${L_2}$.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 240 (1978), 53-64
  • MSC: Primary 55A05; Secondary 57A10
  • DOI:
  • MathSciNet review: 0478129