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Involutive Khovanov homology and equivariant knots
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abstract
For strongly invertible knots, we define an involutive version of Khovanov homology, and from it derive a pair of integer-valued invariants $(\underline{s}, \overline{s})$, which is an equivariant version of Rasmussen's $s$-invariant. Using these invariants, we reprove that the infinite family of knots $J_n$ introduced by Hayden each admits exotic pairs of slice disks. Our construction is intended to give a Khovanov-theoretic analogue of the formalism given by Dai, Mallick and Stoffregen in involutive knot Floer theory.
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Involutive Khovanov homology and equivariant knots II
An improved tangle algorithm computes involutive Khovanov invariants and shows the Whitehead doubles of two pretzel knots carry an equivariant Rasmussen invariant (0,2), yielding new exotic slice disk pairs.
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