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OP-11745Status unassessedGeometry and topology

Relative trisections · Question 3.1

Trisections and low-dimensional topology · AIMPL workshop record

MSC 57 · Manifolds and cell complexes

Editorial mapping of AIMPL list topic: Trisections and low-dimensional topology. http://aimpl.org/trisections/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

Suppose XX is a smooth, oriented 44-manifold with boundary. Consider an open book decomposition on M=∂XM=\partial X and let TT be a relative trisection for XX corresponding to this open book. What conditions on TT implies that the open book supports a tight contact structure?

Remark: Define a notion of compatibility between trisection and symplectic structure. Find the sufficient conditions on the trisection which implies that it is a geometric filling e.g. symplectic filling with a convex or concave boundary.

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References
  1. [1]Trisections and low-dimensional topology · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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