Work

Embedding 3‐manifolds in spin 4‐manifolds

Year: 2017

Type: article

Abstract: An invariant of orientable 3-manifolds is defined by taking the minimum n such that a given 3-manifold embeds in the connected sum of n copies of S 2 × S 2 , and we call this n the embedding number of the 3-manifold. We give some general properties of this invariant, and make calculations for families of lens spaces and Brieskorn spheres. We show how to construct rational and integral homology spheres whose embedding numbers grow arbitrarily large, and which can be calculated exactly if we assume the 11/8-Conjecture. In a different direction we show that any simply connected 4-manifold can be split along a rational homology sphere into a positive definite piece and a negative definite piece.

Source: Journal of Topology

DOI: 10.1112/topo.12010

Authors: Paolo Aceto, Marco Golla, Kyle Larson

Institutions: HUN-REN Alfréd Rényi Institute of Mathematics, Uppsala University, Michigan 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, European Research Council

Award: RTG: Unified Training in Geometry and Topology