Trisections and low-dimensional topology
March 20 to March 24, 2017
American Institute of Mathematics,
San Jose, California
and Alexander Zupan
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
- The structure of trisections: Which trisections can be classified? What
topics from Heegaard splittings can be successfully and usefully imported to
- 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?
- 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: