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Algebra/Topology Seminar – Jonathan Simone (Georgia Institute of Technology)
October 6, 2021 @ 11:00 am - 12:00 pm
Title: The non-orientable 4-ball genus of torus knots
Abstract: The non-orientable 4-ball genus of a knot $K$ in $S^3$ is the minimal first Betti number of any smoothly embedded non-orientable surface in $B^4$ bounded by K. This is the non-orientable analog of the 4-ball genus of $K$ (i.e. the minimal genus of any smooth orientable surface in $B^4$ with boundary K). For torus knots, the 4-ball genus is known, whereas the non-orientable 4-ball genus is not well understood. In this talk, we will give new lower bounds for the non-orientable 4-ball genus of torus knots and calculate the non-orientable 4-ball genus for some infinite families of torus knots. This work is joint with Fraser Binns, Sungkyung Kang, and Paula Truol.