Contact cut graph and Weinstein L-invariant

Curves on surfaces have been very effective in understanding topology of 3- and 4-manifolds, for example Heegaard diagrams, Lefschetz fibrations and trisection/multisection diagrams. I will talk about an analogous way to understand contact and symplectic topology in dimension 3 and 4, called the contact cut graph. We show that each path in the contact cut graph corresponds to a Weinstein domain, from which we define a new invariant for Weinstein domains called the Weinstein L-invariant. We also give some examples of L=0 and L arbitrarily large Weinstein domains. This is joint work with N. Castro, G. Islambouli, S. Sakalli, L. Starkston and A. Wu.

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