dorsal/arxiv
View SchemaDistinguishing exotic $\mathbb{R}^4$'s with Heegaard Floer homology
| Authors | Sean Eli, Jennifer Hom, Tye Lidman |
|---|---|
| Categories | |
| ArXiv ID | 2601.08767vv1 |
| URL | https://arxiv.org/abs/2601.08767 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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.
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"abstract": "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 $\\mathbb{R}^4$\u0027s made using the simplest positive Casson handle are not diffeomorphic, giving us a countably infinite family of pairwise nondiffeomorphic chiral exotic $\\mathbb{R}^4$\u0027s. Our main tool is Gadgil\u0027s 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.",
"arxiv_id": "2601.08767",
"authors": [
"Sean Eli",
"Jennifer Hom",
"Tye Lidman"
],
"categories": [
"math.GT"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Distinguishing exotic $\\mathbb{R}^4$\u0027s with Heegaard Floer homology",
"url": "https://arxiv.org/abs/2601.08767",
"version": "v1"
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