Knots with critical bridge spheres

Puttipong Pongtanapaisan (University of Iowa)

David Bachman introduced the notion of critical surfaces and showed that they satisfy useful properties. In particular, they behave like incompressible surfaces and strongly irreducible surfaces. In this talk, I will review some techniques that have been used to study bridge spheres and give examples of nontrivial knots with critical bridge spheres. This is joint work with Daniel Rodman.

References:

Pongatanpaisan, P., Rodman, D., Critical Bridge Spheres for Links with Arbitrarily Many Bridges, https://arxiv.org/pdf/1906.03483.pdf