Abstract

POMMERENKE, CHRISTIAN  and  TORO, MARGARITA. On the Two-Parabolic Subgroups of SL(2,\mathbbC). Rev.colomb.mat. [online]. 2011, vol.45, n.1, pp.37-50. ISSN 0034-7426.

We consider homomorphisms H_t from the free group F of rank 2 onto the subgroup of SL(2,C) that is generated by two parabolic matrices. Up to conjugation, H_t depends only on one complex parameter t. We study the possible relators, that is, the words w∈ F with w≠ 1 such that H_t(w)=I for some t∈C. We find several families of relators. Of particular interest here are relators connected with 2-bridge knots, which we consider in a purely algebraic setting. We describe an algorithm to determine whether a given word is a possible relator.

Keywords : Representation; Parabolic; Wirtinger presentation; Two-generated groups; Homomorphism; Longitude.

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