We provide new evidence that the tangle calculus and “evolution” are applicable to the
Khovanov polynomials for families of long braids inside the knot diagram. We show that …

Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider
an analogue of this conjecture for slice disks in the four-ball: two slice disks of a knot are …

Thin links and Conway spheres Page 1 Thin links and Conway spheres Artem Kotelskiy,
Liam Watson and Claudius Zibrowius Compositio Math. 160 (2024), 1467–1524. doi:10.1112/S0010437X24007152 …

We show that a large class of satellite operators are rank-expanding; that is, they map some
rank-one subgroup of the concordance group onto an infinite linearly independent set. Our …

We give a family of slice-torus invariants ss˜ c, each defined from the c-divisibility of the
reduced Lee class in a variant of reduced Khovanov homology, parameterized by prime …

We describe a simple formula for computing the Heegaard Floer multicurve invariant of
double tangles from the Heegaard Floer multicurve invariant of knot complements. A …

From Khovanov homology, we extract a new lower bound for the Gordian distance of knots,
which combines and strengthens the previously existing bounds coming from Rasmussen …

The slicing degree of a knot $ K $ is defined as the smallest integer $ k $ such that $ K $ is $
k $-slice in $\#^ n\overline {\mathbb {CP}^ 2} $ for some $ n $. In this paper, we establish …