The classification of compact simply connected biquotients in dimension 4 and 5

TL;DR

This paper classifies all compact simply connected biquotients in dimensions 4 and 5, detailing the group pairs and embeddings that produce these biquotients.

Contribution

It provides a complete classification of such biquotients in low dimensions, including the group pairs and embeddings involved.

Findings

All such biquotients in dimensions 4 and 5 are classified.

Explicit descriptions of group pairs and embeddings are provided.

The classification aids understanding of low-dimensional biquotient geometry.

Abstract

We classify all compact simply connected biquotients of dimension 4 and 5. In particular, all pairs of groups $(G,H)$ and embeddings $H\rightarrow G\times G$ giving rise to a particular biquotient are classified.