Canonical links associated to curves on surfaces
Canonical links associated to curves on surfaces
In-Person and Online Talk听
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Let S be a surface of negative听Euler characteristic and C a collection of closed curves. The set of tangent lines to C is a link in the projective tangent bundle PT(S) and drilling this link, we obtain a 3-manifold M_C. Any invariant of M_C is automatically a mapping class group invariant of C. Further, M_C uniquely determines this mapping class group orbit. In this talk, we will go over results that explain the听behavior and provide coarse bounds on the hyperbolic volume of M_C 听in terms of topological and geometric properties of the family C. For听example, when C听is a filling pair of simple closed curves, we show that the volume is coarsely comparable to Weil-Petersson听distance between strata in Teichmuller space. Lastly, we will explain algorithmic methods and tools for building such links and听computing other invariants. This work is joint with Tommaso Cremaschi, Jacob Intrater, 听and Jose Andres Rodriguez-Migueles.
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