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2008 All $2$–dimensional links in $4$–space live inside a universal $3$–dimensional polyhedron
Cherry Kearton, Vitaliy Kurlin
Algebr. Geom. Topol. 8(3): 1223-1247 (2008). DOI: 10.2140/agt.2008.8.1223

Abstract

The hexabasic book is the cone of the 1–dimensional skeleton of the union of two tetrahedra glued along a common face. The universal 3–dimensional polyhedron UP is the product of a segment and the hexabasic book. We show that any closed 2–dimensional surface in 4–space is isotopic to a surface in UP. The proof is based on a representation of surfaces in 4–space by marked graphs, links with double intersections in 3–space. We construct a finitely presented semigroup whose central elements uniquely encode all isotopy classes of 2–dimensional surfaces.

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Cherry Kearton. Vitaliy Kurlin. "All $2$–dimensional links in $4$–space live inside a universal $3$–dimensional polyhedron." Algebr. Geom. Topol. 8 (3) 1223 - 1247, 2008. https://doi.org/10.2140/agt.2008.8.1223

Information

Received: 7 April 2008; Revised: 7 June 2008; Accepted: 13 June 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1151.57027
MathSciNet: MR2443242
Digital Object Identifier: 10.2140/agt.2008.8.1223

Subjects:
Primary: 57Q35, 57Q37, 57Q45

Rights: Copyright © 2008 Mathematical Sciences Publishers

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