Bar-Natan Modules and Tunneling Graphs
We describe a general method for presentations of colimit modules of functors into module categories. This is applied to the Bar-Natan functor, which is defined on a category of surfaces embedded in a 3-manifold M with morphisms defined by certain 3-manifolds embedded in M x [0,1] and takes values in a category of modules defined from a commutative Frobenius algebra. The colimit of the Bar-Natan functor is the Bar-Natan module of M. Our approach naturally leads to the definition of the tunneling graph of M, which contains the geometric data necessary to deduce the structure of the Bar-Natan module.
Uwe Kaiser. "Bar-Natan Modules and Tunneling Graphs" American Mathematical Society, Spring Western Section Meeting. Las Vegas, NV. May. 2011.
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