On the twisted Alexander polynomial for metabelian represetations into SL(2, C)

Details On the twisted Alexander polynomial for metabelian represetations into SL(2, C) On the twisted Alexander polynomial for metabelian represetations into SL(2, C)

2011-01-20

arxiv.org/abs/1101.3989v2

Mathematics

Geometric Topology

19 pages, 5 figures; V2: expositions improved, one reference added and one theorem added, which relates two kind of twisted Al

Scientific paper

We give explicit forms of the twisted Alexander invariant for metabelian representations of knot groups into $\SL$ and study relations between these computation results and the characterizations of metabelian representations in the character varieties. We also compare the twisted Alexander invariant for metabelian representations with that for the composition with the adjoint action on $\sll$. For irreducible metabelian representations, we show the difference and relation between these two kinds of the twisted Alexander polynomials.

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