Two-bridge knots and their crosscap numbers

Cornelia Van Cott (University of San Francisco)

Begin with two knots K and J. Simon conjectured that if the knot group of K surjects onto that of J, then the genera of the orientable surfaces that the two knots bound are constrained. Specifically, he conjectured g(K) \geq g(J), where g(K) denotes the genus of K. This conjecture has been proved for alternating knots and can be strengthened to an even stronger result in the case of two-bridge knots. In this talk, we consider the same sorts of questions, but in the world of nonorientable surfaces. We focus on two-bridge knots and find relationships among their crosscap numbers. This is joint work with Jim Hoste and Pat Shanahan.


Hoste, J., Shanahan, P., Van Cott, C., “Crosscap number and the partial order on two-bridge knots”,

Further Reading:

One thought on “Two-bridge knots and their crosscap numbers

  1. Thank you, Cornelia, for a fascinating talk! To leave a question for our speaker, please reply to this comment below.

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