An infinite-rank summand of knots with trivial Alexander polynomial

Min Hoon Kim; Kyungbae Park

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arXiv · 1604.04037

An infinite-rank summand of knots with trivial Alexander polynomial

Min Hoon Kim·Kyungbae Park

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Abstract

We show that there exists a $\mathbb{Z}^\infty$-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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Min Hoon Kim, Kyungbae Park. 2016-04-14. An infinite-rank summand of knots with trivial Alexander polynomial. https://arxiv.org/abs/1604.04037

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