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P. Kirk 4-14-2022

Title:  Holonomy perturbed SU(2) character varieties of tangles.
Abstract:  One approach to produce topological invariants of low-dimensional manifolds by a 2-step process, the first step applies the SU(2) character variety functor, which converts surfaces into (singular) symplectic manifolds, and converts 3-manifolds with boundary into Lagrangian immersions. The second step applies Lagragian Floer homology to the resulting Lagrangian immersion. The Atiyah-Floer conjecture posits an identification of the resulting theory with instanton homology. In order to be sensible, the first step requires the use of holonomy perturbations of Taubes and Donaldson to make flat moduli spaces smooth. This talk will describe several explicit calculations of holonomy perturbed character varieties, and how to extract topological information from them, summarizing ideas worked out in several articles co-authored with Cazassus, Kotelskiy, Herald, Hedden, and Hogancamp.

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