# Kauffman states and Heegaard diagrams for tangles

@article{Zibrowius2019KauffmanSA, title={Kauffman states and Heegaard diagrams for tangles}, author={Claudius Zibrowius}, journal={Algebraic \& Geometric Topology}, year={2019} }

We define polynomial tangle invariants $\nabla_T^s$ via Kauffman states and Alexander codes and investigate some of their properties. In particular, we prove symmetry relations for $\nabla_T^s$ of 4-ended tangles and deduce that the multivariable Alexander polynomial is invariant under Conway mutation. The invariants $\nabla_T^s$ can be interpreted naturally via Heegaard diagrams for tangles. This leads to a categorified version of $\nabla_T^s$: a Heegaard Floer homology $\widehat{\operatorname…

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