Trisections and low-dimensional topology

March 20 to March 24, 2017

at the

American Institute of Mathematics, San Jose, California

organized by

David Gay, Robion Kirby, Jeffrey Meier, and Alexander Zupan

Original Announcement

This workshop will be devoted to a new perspective on 4-dimensional topology introduced by Gay and Kirby in 2012: Every smooth 4-manifold can be decomposed into three simple pieces via a trisection, a generalization of a Heegaard splitting of a 3-manifold. Since 2012, the theory of trisections has expanded to include the relative settings of surfaces in 4-manifolds and 4-manifolds with boundary, and tantalizing evidence reveals that trisections may bridge the gap between 3- and 4-dimensional topology. The goal of this workshop is to bring together researchers in low-dimensional topology in order to study interactions between trisections and other powerful tools and techniques.

The main topics for the workshop are

  1. The structure of trisections: Which trisections can be classified? What topics from Heegaard splittings can be successfully and usefully imported to study trisections?
  2. Invariants from trisections: How can invariants coming from Heegaard Floer and Khovanov homology theories and/or contact/symplectic topology be adapted to obtain invariants computed from trisections?
  3. Bridge trisections: How do bridge trisections expand our understanding of knotted surfaces in 4-space? How can bridge trisections be used to apply ideas from classical knot theory to knotted surfaces?

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

The trisection genus of standard simply connected PL 4-manifolds
by  Jonathan Spreer, and Stephan Tillmann
Calculating the homology and intersection form of a 4-manifold from a trisection diagram
by  Peter Feller, Michael Klug, Trent Schirmer, and Drew Zemke
Computing trisections of 4-manifolds
by  Mark Bell, Joel Hass, J. Hyam Rubinstein, and Stephan Tillmann