for this workshop
Trisections and low-dimensional topology
American Institute of Mathematics, San Jose, California
David Gay, Robion Kirby, Jeffrey Meier, and Alexander Zupan
This workshop, sponsored by AIM and the NSF, 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?
The workshop will differ from typical conferences in some regards. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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