Virtual representations for closed graph manifolds and Seifert geometry

TL;DR

This paper investigates the representations of closed graph manifolds into the Seifert motion group, revealing that some graph manifolds do not admit faithful representations into this group, even virtually.

Contribution

It demonstrates the existence of graph manifolds that virtually lack faithful representations into the Seifert motion group, advancing understanding of their geometric structures.

Findings

Some closed graph manifolds have no faithful representations virtually.

The paper establishes conditions under which such representations do not exist.

It contributes to the classification of graph manifolds based on their representability.

Abstract

In this paper, we mainly discuss the representations of closed graph manifolds to the Seifert motion group. Then we prove that there exist graph manifolds virtually having no faithful representations to the Seifert motion group.