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Transactions of the American Mathematical Society

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



The conjugacy problem for boundary loops in $3$-manifolds

Author: Benny D. Evans
Journal: Trans. Amer. Math. Soc. 240 (1978), 53-64
MSC: Primary 55A05; Secondary 57A10
MathSciNet review: 0478129
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Abstract: 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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Keywords: Free homotopy, sufficiently large 3-manifold, conjugacy problem
Article copyright: © Copyright 1978 American Mathematical Society