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Combinatorial and Gauge theoretical methods in low dimensional topology and geometry

Knot traces and L-spaces

speaker: Steven Sivek (Imperial College London)

abstract: Given any knot $K$ and integer $n$, we form the $n$-trace $X_n(K)$ by attaching an $n$-framed 2-handle to the 4-ball along $K$. We will show that for any choice of $n \geq 0$, the oriented diffeomorphism type of $X_n(K)$ determines the hat Heegaard Floer homologies of all nonnegative rational surgeries on $K$. We will then use this to show that every torus knot is detected by its 0-trace. This is joint work with John Baldwin.

timetable:
Wed 5 Jun, 9:30 - 10:30, Aula Dini
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