Title: Skein valued open Gromov-Witten invariants and cluster mutations
Abstract: We consider a class of Lagrangians living in \mathbb{C}^3 . Their Ekholm-Shende wavefunctions, living in the HOMFLY-PT skein module, will encode open Gromov-Witten invariants in all genus and arbitrarily many boundary components. We develop a skein valued cluster theory to compute these wavefunctions. In some simple cases, our computation matches up with the topological vertex. Along the way we define a skein dilogarithm and prove a pentagon relation, which will imply the 5-term relation of Garsia and Mellit, originally formulated in terms of Macdonald polynomials.
Eric Zaslow
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