The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase

Matthew Hedden; Christopher M. Herald; Paul Kirk

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arXiv · 1501.00028

The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase

Matthew Hedden·Christopher M. Herald·Paul Kirk

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Abstract

We define an elementary relatively $\mathbb Z/4$ graded Lagrangian-Floer chain complex for restricted immersions of compact 1-manifolds into the pillowcase, and apply it to the intersection diagram obtained by taking traceless $SU(2)$ character varieties of 2-tangle decompositions of knots. Calculations for torus knots are explained in terms of pictures in the punctured plane. The relation to the reduced instanton homology of knots is explored.

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Matthew Hedden, Christopher M. Herald, Paul Kirk. 2014-12-30. The pillowcase and traceless representations of knot groups II: a Lagrangian-Floer theory in the pillowcase. https://arxiv.org/abs/1501.00028

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