The complement of the Bowditch space in the SL(2,C) character variety

Details The complement of the Bowditch space in the SL(2,C) character variety The complement of the Bowditch space in the SL(2,C) character variety

2006-03-17

arxiv.org/abs/math/0603418v1

Osaka J. Math. Volume 44, Number 2 (2007), 247-254

Mathematics

Geometric Topology

6 pages

Scientific paper

Let ${\mathcal X}$ be the space of type-preserving $\SL(2,C)$ characters of the punctured torus $T$. The Bowditch space ${\mathcal X}_{BQ}$ is the largest open subset of ${\mathcal X}$ on which the mapping class group acts properly discontinuously, this is characterized by two simple conditions called the $BQ$-conditions. In this note, we show that $[\rho]$ is in the interior of the complement of ${\mathcal X}_{BQ}$ if there exists an essential simple closed curve $X$ on $T$ such that $|{\rm tr} \rho(X)|<0.5$.

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