The conjecture on arbitrarily large topological four-genus of algebraically slice GA-knots

A GA-knot is a knot that can be written as a connected sum of algebraic knots and their reverse mirror images. A knot is algebraically slice if it bounds a genus-zero surface in a suitable algebraic concordance sense, and its topological four-genus is the minimum genus of a locally flat surface it bounds in the topological four-ball.

Arbitrarily large four-genus conjecture. There are algebraically slice GA-knots with arbitrary large topological four-genus.

The conjecture asks whether the known examples of algebraically slice, non-slice GA-knots, whose topological four-genus is one, can be extended to examples with no universal bound on their topological four-genus.