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

Abstract

We define an elementary relatively ℤ/4 Z / 4 graded Lagrangian–Floer chain complex for restricted immersions of compact 1 1 -manifolds into the pillowcase, and apply it to the intersection diagram obtained by taking traceless SU(2) S U ( 2 ) character varieties of 2 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.