Companionship and Knot Group Representations
نویسنده
چکیده
A companionship argument is used to give a constructive geometric proof of a key result concerning the knot homomorph problem: Given elements p and A in a group G, is there a knot K in S3 and a surjective representation p : n,(S3 K) + G, such that p(m) = y and p( [) = A, where m and I are the meridian and longitude of K. The result presented here is that if for some p that normally generates G, the pair (CL, +“) is realizable, where n is the order of H,(G; Z), then the pair (v, v”) is realizable for any normal generator Y.
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