Signed clasp numbers and four-genus bounds

Abstract

There exist knots having positive and negative four-dimensional clasp numbers zero but having four-genus, and hence clasp number, arbitrarily large. Such examples were first constructed by Allison Miller, answering a question of Juhasz-Zemke. Further examples are constructed here, complementing those of Miller in that they include examples that are of infinite order in concordance.

Exposition revised, figure added