Knots in the curve graph

Abstract:

By a famous theorem of Thurston the space \(\PML\) of projective (measured) laminations on a five-times punctured sphere is a three-sphere. An elementary example of a projective lamination is a simple closed geodesic with the counting measure. This defines a map from the set of curves to \(\PML\), which extends to an injective map from the curve graph to \(\PML\). The topology of the image of the curve graph in \(\PML\) and its complement were previously studied by Gabai.

In this talk we will introduce certain finite subgraphs of the curve graph of the five-times punctured sphere and determine whether their image in \(\PML\) is knotted.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | slides )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

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