Conference Proposal - Structure of 3-manifold Groups

Tufts University, Medford MA

Investigators

Abstract

The conference, "Structure of 3-manifold groups" will be held in Marseille, Luminy (France) at the Centre International de Rencontres Mathematiques (CIRM) from February 26 to March 2, 2018. The organizers expect that the meeting will have about 90 participants. The award funds participation of US based mathematicians in this event. The topics covered at the conference are of high current interest with difficult outstanding problems. There have recently been new techniques developed regarding this family of problems and related conjectures regarding the structure of 3-manifold groups. The organizers expect that bringing mathematicians together from different areas with different points of view regarding these topics will serve mathematical progress. This conference is part of a semester whose aim is to foster international collaboration, particularly between the United States and France. There is time allowed for interaction and collaboration, and the mix of senior and junior mathematicians should be very productive. The conference will focus on determining which groups are the fundamental groups of 3-manifolds. Understanding which groups are 3-manifold groups is a very old problem, but there are new ways of thinking about groups that allow to make progress in certain cases. In particular, much progress has been made in the field of relatively hyperbolic groups, and specific classes of hyperbolic groups, such as free-by-cyclic groups. Specifically, the conference will cover topics about Poincare duality groups, when certain classes of groups are the fundamental groups of 3-manifolds, pro-finite completions of groups, surface subgroups of groups, and decompositions of groups analogous to decompositions of 3-manifolds. The main goal is that specific results will be obtained by bringing individuals together. There is a continuously evolving website for the meeting at https://walsh-paoluzzi.weebly.com/conference.html. In particular, interested participants can pre-register at that site.