| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

3. Relative trisections


    1. Add remark

      Problem 3.1.

      Suppose $X$ is a smooth, oriented $4$-manifold with boundary. Consider an open book decomposition on $M=\partial X$ and let $T$ be a relative trisection for $X$ corresponding to this open book. What conditions on $T$ 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.


        • Add remark

          Problem 3.2.

          For $4$-manifolds with boundary, how trisection genus changes under boundary connected sum?

              Cite this as: AimPL: Trisections and low-dimensional topology, available at http://aimpl.org/trisections.