2022/10/19 by Sally Collins, Collins, Sally · 1 citation
Mathematics · Medicine · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Botulinum Toxin and Related Neurological Disorders
paper · pdf · doi:10.48550/arxiv.2210.10308
The 0-surgeries of two knots K1 and K2 are homology cobordant rel meridians if there exists a ℤ-homology cobordism X between them such that the two knot meridians are in the same homology class in H1(X,ℤ). In this paper, we give a pair of rationally slice knots which are not smoothly concordant but whose 0-surgeries are homology cobordant rel meridians. One knot in the pair is the figure eight knot, which has concordance order two; all previous examples of such pairs of knots are infinite order.