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math.GT2026
Deeply Slice Knot Detection via Immersed Curves
Rob McConkey, Christopher St. Clair, Tristan Wells +1
On the Kirby list, Akbulut poses the question of whether there exists a homology 3-sphere , other than , with the following property: Any knot , representing $0\inÏ_{1}…
math.GT2025
Satellite Operations and
Rob McConkey, Luke J Seaton
We study the behavior of the knot invariant under satellite operations. First, we prove that is additive under connected sum. We then introduce a computational tool to ge…
math.GT2024
Crossing numbers of cable knots
Efstratia Kalfagianni, Rob Mcconkey
We use the degree of the colored Jones knot polynomials to show that the crossing number of a -cable of an adequate knot with crossing number is larger than . A…