An obstruction to embedding $2$-dimensional complexes into the $3$-sphere
Geometric Topology
2015-03-31 v2 Algebraic Topology
Combinatorics
Abstract
We consider an embedding of a -dimensional CW complex into the -sphere, and construct it's dual graph. Then we obtain a homogeneous system of linear equations from the -dimensional CW complex in the first homology group of the complement of the dual graph. By checking that the homogeneous system of linear equations does not have an integral solution, we show that some -dimensional CW complexes cannot be embedded into the 3-sphere.
Cite
@article{arxiv.1503.02170,
title = {An obstruction to embedding $2$-dimensional complexes into the $3$-sphere},
author = {Kazufumi Eto and Shosaku Matsuzaki and Makoto Ozawa},
journal= {arXiv preprint arXiv:1503.02170},
year = {2015}
}
Comments
10 page, 11 figures