An infinite-rank summand of knots with trivial Alexander polynomial

2016/04/14 by Kim, Min Hoon, Park, Kyungbae · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1604.04037

Abstract

We show that there exists a ℤ^∞-summand in the subgroup of the knot concordance group generated by knots with trivial Alexander polynomial. To this end we use the invariant Upsilon Υ recently introduced by Ozsváth, Stipsicz and Szabó using knot Floer homology. We partially compute Υ of (n,1)-cable of the Whitehead double of the trefoil knot. For this computation of Υ, we determine a sufficient condition for two satellite knots to have identical Υ for any pattern with nonzero winding number.

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