Eine Bemerkung zu einigen $2$-dimensionalen Komplexen, die im $\mathbb{R}^4$ fast-eingebettet werden k\"onnen

TL;DR

The paper demonstrates that many 2-complexes from Freedman-Krushkal-Teichner's work can be PL immersed in R^4 with only self-intersections of 2-cells, providing insight into their embedding properties.

Contribution

It shows that these 2-complexes can be almost-embedded in R^4 with controlled singularities, advancing understanding of their topological embedding behavior.

Findings

Many complexes can be PL immersed in R^4 with disjoint cell interiors.

Self-intersections are limited to some 2-cells, not the entire complex.

Supports the idea of almost-embedding in low-dimensional topology.

Abstract

We observe that many of the 2-complexes constructed by Freedman-Krushkal-Teichner in their paper on the incompleteness of the van Kampen embedding obstruction can actually be PL immersed in $\mathbb{R}^4$ in such a way that the images of the interiors of distinct cells are disjoint. In other words, they PL almost-embed in $\mathbb{R}^4$ with singularities occurring only as self intersections of some 2-cells. This note is written in (not necessarily modern) German.