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

摘要

We define an elementary relatively $mathbb Z/4$ graded Lagrangian-Floerchain complex for restricted immersions of compact 1-manifolds into thepillowcase, and apply it to the intersection diagram obtained by takingtraceless $SU(2)$ character varieties of 2-tangle decompositions of knots.Calculations for torus knots are explained in terms of pictures in thepunctured plane. The relation to the reduced instanton homology of knots isexplored.