Journal of Symplectic Geometry

Volume 16 (2018)

Number 6

An infinite-rank summand of knots with trivial Alexander polynomial

Pages: 1749 – 1771



Min Hoon Kim (School of Mathematics, Korea Institute for Advanced Study, Seoul, South Korea)

Kyungbae Park (Department of Mathematical Sciences, Seoul National University, Seoul, South Korea)


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. We use the $\Upsilon$-invariant introduced by Ozsváth, Stipsicz and Szabó. For our computation, we give a sufficient condition for two satellite knots to have the identical $\Upsilon$-invariant.

Received 19 April 2016

Accepted 23 February 2018

Published 18 March 2019