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
- The structure of trisections: Which trisections can be classified? What
topics from Heegaard splittings can be successfully and usefully imported to
study trisections?
- 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:
