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.
The Farrell-Jones conjecture for free-by-cyclic groups – VIDEO
Deforming foliations in branched covers and the L-space conjecture
Mapping Class Groups do not have deep relations (between Dehn twists)
Product set growth in hyperbolic geometry
Median geometry for lattices
Profinite completions of fundamental groups and discrete approximations of simplicial volume
The 4-Dimensional Light Bulb Theorem
Homomorphisms to 3-manifold groups and other families – VIDEO
Poincaré duality in dimension 3
Diffeomorphism groups of critical regularity
One-ended 3-manifolds without locally finite toric decompositions
Profinite rigidity in low dimensions
The visual boundary of hyperbolic free-by-cyclic groups – VIDEO
Groups with Bowditch boundary a 2-sphere – VIDEO
Relative cohomology, profinite completions and 3-manifold decompositions
Negative immersions for one-relator groups