Work

Exotic families of embeddings

Year: 2025

Type: preprint

Abstract: We construct a number of topologically trivial but smoothly non-trivial families of embeddings of 3-manifolds in 4-manifolds. These include embeddings of homology spheres in $S^4$ that are not isotopic but have diffeomorphic complements, and families (parameterized by high-dimensional spheres) of embeddings of any 3-manifold that embeds in a blown-up K3 surface. In each case, the families are constructed so as to be topologically trivial in an appropriate sense. We also illustrate a general technique for converting a non-trivial family of embeddings into a non-trivial family of submanifolds.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2501.12673

Authors: Auckly, Dave, Ruberman, Daniel

Institution: Kansas State University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Division of Mathematical Sciences

Awards: Mathematical Sciences Research Institute (MSRI), FRG: Collaborative Research in Gauge Theory, G329468232, Applications of Gauge Theory and Floer Homology to Low-Dimensional Topology, G6019427330, FRG: Collaborative Research in Gauge Theory

OpenAlex ID: W4406779040

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