# Virtually cyclic dimension for 3-manifold groups

## TL;DR

This paper computes the virtually cyclic geometric dimension of fundamental groups of closed, orientable 3-manifolds using decompositions and cohomology tools, advancing understanding of their algebraic and topological properties.

## Contribution

It provides explicit calculations of the virtually cyclic geometric dimension for 3-manifold groups, integrating prime and JSJ decompositions with cohomology methods.

## Key findings

- Explicit formulas for the virtually cyclic dimension
- Application of JSJ decomposition in dimension calculation
- Use of Bredon cohomology in geometric dimension analysis

## Abstract

Let G be the fundamental group of a connected, closed, orientable 3-manifold. We explicitly compute its virtually cyclic geometric dimension. Among the tools we use are the prime and JSJ decompositions of M, several push-out type constructions, as well as some Bredon cohomology computations.