Two-solvable and two-bipolar knots with large four-genera

Abstract

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Strongly invertible knots, equivariant slice genera, and an equivariant algebraic concordance group

“…We remark that items (1), (2), and (3) of Proposition 5.1 are reasonably standard and have appeared in the literature before; see, for example, [38, section 4; 10, Proposition 9.1]. We include the proof of these items here for completeness.…”

“…For the proof of Proposition 5.5, we will need the following result from our article [10] with Jae Choon Cha. Proof of Proposition 5.5.…”

“…For the proof of Proposition 5.5, we will need the following result from our article [10] with Jae Choon Cha. Lemma Let $$X$$ be a compact, oriented 4‐manifold with boundary $$\partial X=Y$$.…”

Slice knots and knot concordance

“…The n = 0 and 1 cases can be shown using Levine-Tristram and Casson-Gordon signatures respectively, while the n = 2 case was shown by Cha-Miller-Powell in [CMP21].…”