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.


Pongatanpaisan, P., Rodman, D., Critical Bridge Spheres for Links with Arbitrarily Many Bridges,

3 thoughts on “Knots with critical bridge spheres

  1. Thank you Puttipong Pongtanapaisan for a great talk! To ask the speaker a question, please respond to this comment below.

    1. This is more of an artistic question that an mathematical one. Could you briefly explain how you drew that absolutely amazing picture at time marker 35:19 (right hand side of the slide)?

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