Kauffman states and Heegaard diagrams for tangles

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