The conjugacy problem for boundary loops in -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 in the boundary of a compact, orientable, irreducible sufficiently large 3-manifold *M* if , is freely homotopic in *M* to .

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0478129-4

Keywords:
Free homotopy,
sufficiently large 3-manifold,
conjugacy problem

Article copyright:
© Copyright 1978
American Mathematical Society