K-Decompositions and 3d Gauge Theories

Understand

This paper combines several new constructions in mathematics and physics.

• Mathematically, we study framed flat PGL(K,C)-connections on a large class of 3-manifolds M with boundary.
• We define a space L_K(M) of framed flat connections on the boundary of M that extend to M.
• Our goal is to understand an open part of L_K(M) as a Lagrangian in the symplectic space of framed flat connections on the boundary, and as a K_2-Lagrangian, meaning that the K_2-avatar of the symplectic form restricts to zero.