Embedding 3‐manifolds in spin 4‐manifolds. Issue 2 (7th April 2017)

• Record Type: Journal Article
• Authors: Aceto, Paolo; Golla, Marco; Larson, Kyle
• Is Part Of: Journal of topology. Volume 10:Issue 2(2017)
• Page Start: 301
• Page End: 323
• Publication Date: 2017-04-07
• Subjects: 57R15 -- 57R40 (primary) -- 57M27 (secondary); Topology -- Periodicals; 514.05
• DOI: 10.1112/topo.12010
• Languages: English
• ISSNs: 1753-8416

Abstract

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.