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Embedding 3-manifolds in spin 4-manifolds
Alfred Renyi Inst Math, Realtanoda Ut 13-15, H-1053 Budapest, Hungary..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
Michigan State Univ, Dept Math, 619 Red Cedar Rd, E Lansing, MI 48824 USA..
2017 (English)In: Journal of Topology, ISSN 1753-8416, E-ISSN 1753-8424, Vol. 10, no 2, 301-323 p.Article in journal (Refereed) Published
Abstract [en]

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 x 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.

Place, publisher, year, edition, pages
WILEY , 2017. Vol. 10, no 2, 301-323 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-326208DOI: 10.1112/topo.12010ISI: 000402092400001OAI: oai:DiVA.org:uu-326208DiVA: diva2:1120925
Funder
EU, European Research CouncilKnut and Alice Wallenberg Foundation
Available from: 2017-07-07 Created: 2017-07-07 Last updated: 2017-07-07Bibliographically approved

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