Annular Rasmussen invariants: Properties and 3-braid classification

19 Sep 2019  ·  Martin Gage ·

We prove that for a fixed braid index there are only finitely many possible shapes of the annular Rasmussen $d_t$ invariant of braid closures. Applying the same perspective to the knot Floer invariant $\Upsilon_K(t)$, we show that for a fixed concordance genus of $K$ there are only finitely many possibilities for $\Upsilon_K(t)$... Focusing on the case of 3-braids, we compute the Rasmussen $s$ invariant and the annular Rasmussen $d_t$ invariant of all 3-braid closures. As a corollary, we show that the vanishing/non-vanishing of the $\psi$ invariant is entirely determined by the $s$ invariant and the self-linking number. read more

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Geometric Topology Quantum Algebra