On the local structure of SL(2,C)-character varieties at reducible characters

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Abstract

We describe a 1-cocycle condition that guarantees the smoothness of a reducible character in the SL(2,C)-character variety of a finitely generated group. This result is then applied to study fillings of one-cusped hyperbolic manifolds which yield Seifert fibred manifolds with Euclidean orbifolds.

Keywords

SL(2,C)-character variety
Reducible
Dehn filling
Seifert fibred
Euclidean orbifold

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Partially supported by grants: NSERC OGP 0009446 and FCAR ER-68657.