Évènement

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?

• ​Ian Agol (University of California, Berkeley)
• Michel Boileau  (Aix-Marseille Université)
• Alan Reid (University of Texas at Austin)

• Peter Haïssinsky (Aix-Marseille Université)
• Luisa Paoluzzi (Aix-Marseille Université)
• Genevieve Walsh (Tufts University & Aix-Marseille University)

• Mladen Bestvina (University of Utah)

The Farrell-Jones conjecture for free-by-cyclic groups – VIDEO

• Steven Boyer (Université du Québec à Montréal)

Deforming foliations in branched covers and the L-space conjecture

• François Dahmani (Université Grenoble Alpes)

Mapping Class Groups do not have deep relations (between Dehn twists)

• Thomas Delzant (Université de Strasbourg)

Product set growth in hyperbolic geometry

• Cornelia Drutu Badea (University of Oxford)

Median geometry for lattices

• Roberto Frigerio (Università di Pisa)

Profinite completions of fundamental groups and discrete approximations of simplicial volume

• David Gabai (Princeton University)

The 4-Dimensional Light Bulb Theorem

• ​Daniel Groves (University of Illinois at Chicago)

Homomorphisms to 3-manifold groups and other families – VIDEO

• Jonathan Hillman (University of Sydney)

Poincaré duality in dimension 3

• Sang-Hyun Kim (Seoul National University)

Diffeomorphism groups of critical regularity

• Sylvain Maillot (Université de Montpellier)

One-ended 3-manifolds without locally finite toric decompositions

• Alan Reid (Rice University)

Profinite rigidity in low dimensions

• Emily Stark (Technion)

The visual boundary of hyperbolic free-by-cyclic groups – VIDEO

• Bena Tshishiku (Harvard)

Groups with Bowditch boundary a 2-sphere – VIDEO

• Gareth Wilkes (Oxford University)

Relative cohomology, profinite completions and 3-manifold decompositions

• Henry Wilton (University of Cambridge)

Negative immersions for one-relator groups