Lifting representations of Z-groups

Details Lifting representations of Z-groups Lifting representations of Z-groups

2004-05-24

arxiv.org/abs/math/0405457v2

Mathematics

Geometric Topology

Version 2 has a new example 3.6 and other small revisions. To appear in Israel J. Math. Plain TeX, 14 pages with 1 eps figure

Scientific paper

Let K be the kernel of an epimorphism G -> Z, where G is a finitely presented group. If K has infinitely many subgroups of index 2, 3, or 4, then it has uncountably many. Moreover, if K is the commutator subgroup of a classical knot group G, then any homomorphism from K onto the symmetric group S_2 lifts to a homomorphism onto S_3, and any homomorphism from K onto Z_3 lifts to a homomorphism onto the alternating group A_4.

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