Non-slice linear combinations of algebraic knots

TL;DR

This paper investigates the structure of the knot concordance group, showing that the subgroup generated by links of isolated complex singularities intersects with algebraically slice knots in an infinitely generated subgroup.

Contribution

It demonstrates the existence of an infinite rank subgroup within the intersection of these two significant subgroups in the knot concordance group.

Findings

The subgroup generated by links of isolated complex singularities is large.

The intersection with algebraically slice knots contains an infinite rank subgroup.

Provides new insights into the structure of the knot concordance group.

Abstract

We show that the subgroup of the knot concordance group generated by links of isolated complex singularities intersects the subgroup of algebraically slice knots in an infinite rank subgroup.