arXiv subjects

Sean Eli

Publications and source records attributed to Sean Eli.

3 recordsLinked to original sources

arXiv2026

Irreducible proper 2-knots from exotic open 2-handles

We construct infinite families of irreducible exotic proper knotted surfaces in $\mathbb{R}^4$, making progress on a question of Gompf. Here irreducible means these surfaces are not end-sums of standard surfaces with exotic planes. To prove the topological equivalence, we give a highly flexible construction of exotic open 2-handles, which generalizes several similar constructions in the literature. We distinguish exotic surfaces through the genus functions and end Floer homology of their double branched covers. By studying these generalized handles further, we construct a new family of topologically slice links.

math.GT↗

arXiv2026

Exotic $\mathbb{R}^4$'s, RBG Links, and End Floer Homology

We give the first pair of non-diffeomorphic exotic $\mathbb{R}^4$'s made by attaching diffeomorphic Casson handles onto diffeomorphic disk complements. Our examples are obtained using the RBG link construction to find slice knots with diffeomorphic slice disk complements, but whose Whitehead doubled disk complements are not diffeomorphic. We distinguish the exotic $\mathbb{R}^4$'s using end Floer homology.

math.GT↗

arXiv2026

Distinguishing exotic $\mathbb{R}^4$'s with Heegaard Floer homology

Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to $\mathbb{R}^4$. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic $\mathbb{R}^4$'s made using the simplest positive Casson handle are not diffeomorphic, giving us a countably infinite family of pairwise nondiffeomorphic chiral exotic $\mathbb{R}^4$'s. Our main tool is Gadgil's end Floer homology and we use this to produce families of exotic $\mathbb{R}^4$ with various phenomena. As an application, we reprove a result of Bi\v{z}aca-Etnyre that $Y \times \mathbb{R}$, where $Y$ is any closed $3$-manifold, has infinitely many distinct smooth structures.

math.GT↗