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2. Bridge trisections

    1. Problem 2.1.

      Show the following families of are standard:
      1. (a) $(b;1)$-bridge trisections (Remark: These surfaces have cyclic $\pi_1$ so interesting surfaces in this family are exotic.)
      2. (b) $(b;b-1)$-bridge trisections (Remark: Trisections of the double branched covers are trivial.)
      3. (c) $(b;c,b-c+1,1)$-bridge trisections (Remark: These surfaces have a single max (min).)
        • Problem 2.2.

          Find new invariants of knotted surfaces using Heegaard Floer homology techniques.
            • Problem 2.3.

              Find Khovanov type invariants coming from bridge trisections of knotted surfaces.
                • Problem 2.4.

                  Find Casson type invariants (based on character variety representations) of knotted surfaces.
                    • Problem 2.5.

                      Find skein theoretic invariants of knotted surfaces.
                        • Problem 2.6.

                          Can we use trisections to study knotted concordances?
                            • Problem 2.7.

                              Classify trivial tangles which have two different plat closures to unlink.

                              (Remark: Generate examples of bridge trisections)

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