Mark Hughes

collaborators

3 papers

math.GT2026

An irreducible real projective plane in the 4-sphere

Mark Hughes, Seungwon Kim, Maggie Miller +1

We construct an irreducible embedded projective plane in $S^{4}$ . This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, w…

math.GT2025

Branched Covers of Open Manifolds

Mark Hughes, Alexandra Kjuchukova, Maggie Miller

For $m = 2$ and $m = 3$ we prove that any connected, oriented, open manifold $M^{m}$ admits a simple branched covering map over $R^{m}$ . When $M$ has $k$ ends and $k$ is finite, t…

math.GT2025

Branched covers of twist-roll spun knots and turned twisted tori

Mark Hughes, Seungwon Kim, Maggie Miller

We prove that the double branched cover of a twist-roll spun knot in $S^{4}$ is smoothly preserved when four twists are added, and that the double branched cover of a twist-roll spun…