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

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Paul Kirk
MPIM/IU Bloomington
Mon, 05/09/2022 - 15:15 - 16:00
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

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.


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