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Paul Kirk

The holonomy perturbed SU(2) character variety of the earring tangle
Lundi, 11 Juillet, 2022 - 10:00 à 11:00
Résumé : 

One of the prominent roles played by SU(2) character varieties of closed 3-manifolds is as the generating set of the Instanton Floer complex, defined as the Morse complex of the Chern-Simons functional.  A profound connection to the construction of Topological quantum field theories is provided by the Atiyah-Floer conjecture, which connects Instanton homology to the Lagrangian-Floer homology of the SU(2) character varieties.   I will discuss extensions of these ideas to pairs (M,T) where T is a tangle in a 3-manifold, and describe explicitly an example of the holonomy perturbed character variety of a certain “atom” (in the sense of Kronheimer-Mrowka) called the earring. 
The calculation is then described in terms of its action on the Fukaya A_infty category of the SU(2) character variety of the 4-punctured 2-sphere.   (joint work with Cazassus, Herald, and Kotelskiy)

Institution de l'orateur : 
Indiana University
Thème de recherche : 
Salle : 
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