Planar diagrams for local invariants of graphs in surfaces

Preprint, 2018, with Kyle Miller

In order to apply quantum topology methods to non-planar graphs, we define a planar diagram category that describes the local topology of embeddings of graphs into surfaces. We also discuss an extension of the flow polynomial called the S-polynomial and relate it to the Yamada and Penrose polynomials.

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What is Lie algebra cohomology and why should you care?

Expository notes on Lie algebra cohomology. The goal is to build up the theory in as concrete a manner as possible, motivated by basic structure theorems for Lie algebras.

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