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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.