Sebastian Baader, Levi Ryffel
Published 2023-10-18Version 1
We determine the cobordism distance between all positive 3-braid links and connected sums of trefoil knots, up to a constant error. This may be seen as a reinterpretation of Coxeter's finiteness result on the braid group on three strands modulo third powers of the generators. We go on to explore the limits of Coxeter's result, and find the cobordism distance between three strand torus links and almost all connected sums of two strand torus links, up to a constant error.
Comments: 8 pages, 2 figures, comments welcome
The cobordism distance between a knot and its reverse
Cobordism distance on the projective space of the knot concordance group
Characterizing $3$-dimensional manifolds represented as connected sums of Lens spaces, $S^2 \times S^1$, and torus bundles over the circle by certain Morse-Bott functions
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