All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron
Geometric Topology
2014-10-01 v2
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.
Cite
@article{arxiv.0801.3647,
title = {All 2-dimensional links in 4-space live inside a universal 3-dimensional polyhedron},
author = {Cherry Kearton and Vitaliy Kurlin},
journal= {arXiv preprint arXiv:0801.3647},
year = {2014}
}
Comments
18 pages, 18 figures, proofs have been made more detailed