The conjugacy problem for boundary loops in manifolds
Author:
Benny D. Evans
Journal:
Trans. Amer. Math. Soc. 240 (1978), 5364
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 3manifolds has been given by F. Waldhausen. We present here a solution of a restricted version of the conjugacy problem for this same class of 3manifolds; however, the conjugacy problem for 3manifolds 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 3manifold M if , is freely homotopic in M to .
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 M. Dehn, Über unendliche diskontinvierliche Gruppen, Math. Ann. 71 (1911), 116144. MR 1511645
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 C. F. Feustel, The torus theorem and its applications (preprint).
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 W. Haken, Some results on surfaces in 3manifolds, Studies in Modern Topology, Math. Assoc. Amer. (distributed by PrenticeHall, Englewood Cliffs, N. J.), 1968, pp. 3998. MR 36 #7118. MR 0224071 (36:7118)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197804781294
PII:
S 00029947(1978)04781294
Keywords:
Free homotopy,
sufficiently large 3manifold,
conjugacy problem
Article copyright:
© Copyright 1978
American Mathematical Society
