**abstract:**
The crosscap number of a knot is the non-orientable counterpart of its
genus. It is defined as the minimum of one minus the Euler characteristic of
S, taken over all non-orientable surfaces S bounding the knot. Computing the
crosscap number of a knot is tricky, since normal surface theory - the usual
tool to prove computability of problems in 3-manifold topology, does not
deliver the answer "out-of-the-box".
In this talk, I will review the strengths and weaknesses of normal surface
theory, focusing on why we need to work to obtain an algorithm to compute
the crosscap number. I will then explain the theorem stating that an
algorithm due to Burton and Ozlen can be used to give us the answer.
This is joint work with Jaco, Rubinstein, and Tillmann.

Mon 27 Nov, 9:30 - 10:30, Aula Dini

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