Lagragian-Floer homology for traceless character varieties of tangles and the pillowcase, II

Hybrid talk.
Contact for details: Tobias Barthel, Viktoriya Ozornova, Aru Ray, Peter Teichner.

We describe progress towards a bordered Atiyah-Floer counterpart of Kronheimer-Mrowka’s
singular instanton homology, with a focus on 2-tangles in 3-balls and their perturbed traceless character varieties, which are smooth curves in a certain 2-d flat SU(2) moduli space  (called the pillowcase), We further describe a non-trivial morphism induced from the Kronheimer-Mrowka “earring”  tangle from the wrapped Fukaya category of the pillowcase to the (compact) Fukaya category of the pillowcase, and its relation to Khovanov homology.