All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron

Cherry Kearton; Vitaliy Kurlin

doi:10.2140/agt.2008.8.1223

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arXiv · 0801.3647

All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron

Cherry Kearton·Vitaliy Kurlin

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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 2-dimensional link 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 links.

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BibTeX RIS

Cherry Kearton, Vitaliy Kurlin. 2008-04-07. All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron. https://doi.org/10.2140/agt.2008.8.1223

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