Institut de Mathématiques de Marseille, UMR 7373


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Structure of 3-manifold groups

Du 26 février 2018 au 2 mars 2018 -

Structure of 3-manifold groups

Structure of 3-manifold Groups.
Every finitely presented group is the group of a closed 4-manifold. However, 3-manifold groups are special. Part of the goal of this conference will be to understand how special they are. The Wall conjecture asserts that the fundamental groups of closed 3-manifolds are the same as groups which satisfy 3-dimensional Poincaré duality (PD(3) groups). Three-manifolds decompose along spheres and tori and this translates to decompositions of their fundamental groups. There have been very fruitful analogs of this decomposition for more general groups.
The conference will focus on the structure of 3-manifold groups as well as structures on groups inspired by structures on 3-manifolds, such as PD (3) groups, relatively hyperbolic groups and buildings.
We will aim to address some of the following topics, as well as new topics which may arise.
- Which of certain classes of groups, for example limit groups, are 3-manifold groups ?
- Are hyperbolic 3-manifold groups determined by their profinite completions ?
- How are the isometry groups of buildings similar to three-manifold groups ?
- What can the boundaries of hyperbolic buildings tell us about these groups ?
- Can one algorithmically decide if a group is the group of a 3-manifold with boundary ?
- When are relatively hyperbolic groups the fundamental groups of 3-manifolds ?
- How can a surface subgroup inside a group inform us about the structure of that group ?
- Which group-theoretic properties of 3-manifold groups (such as residual finiteness) hold for more general classes of groups ?
5ème semaine. fifth week.

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