2π-graftings and complex projective structures I

Details 2π-graftings and complex projective structures I 2π-graftings and complex projective structures I

2010-11-23

arxiv.org/abs/1011.5051v1

Mathematics

Geometric Topology

68 pages, 15 figures

Scientific paper

Let $S$ be a closed orientable surface of genus at least two, and let $C$ and $C'$ be complex projective structures on $S$ with the same holonomy and orientation. We show that, if, via Thurston's coordinates, the projection of $C'$ to $PML(S)$ is sufficiently close to that of $C$, then $C$ and $C'$ are related by a $2\pi$-grafting along a multiloop $M$. Moreover $M$ is well-approximated by the difference of the measured laminations corresponding to $C$ and $C'$, calculated on a traintrack.

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