English

Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation

Combinatorics 2019-09-05 v3 Geometric Topology

Abstract

This paper is the last paper in a series of five papers. Building on earlier papers in this series, we prove an analogue of Kuratowski's characterisation of graph planarity for three dimensions. More precisely, a simply connected 2-dimensional simplicial complex embeds in 3-space if and only if it has no obstruction from an explicit list of obstructions. This list of obstructions is finite except for one infinite family.

Keywords

Cite

@article{arxiv.1709.04659,
  title  = {Embedding simply connected 2-complexes in 3-space -- V. A refined Kuratowski-type characterisation},
  author = {Johannes Carmesin},
  journal= {arXiv preprint arXiv:1709.04659},
  year   = {2019}
}
R2 v1 2026-06-22T21:42:49.795Z