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

2014/12/30 by Hedden, Matthew, Herald, Christopher M., Kirk, Paul · 2 citations
#57M25 #57R58 #FOS: Mathematics #Geometric Topology (math.GT) #Primary 57M27 #Secondary 81T13

paper · doi:10.48550/arxiv.1501.00028

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.

Cited by

• Traceless SU(2) characters and ℤ/4 instanton gradings for two-bridge and (3,n)-torus knots
• The instanton homology of the (-2,3,q) pretzel knots and computed bounding cochains in the pillowcase

Related

• Bordered theory for pillowcase homology
• Symplectic instanton knot homology
• Traceless SU(2) characters and ℤ/4 instanton gradings for two-bridge and (3,n)-torus knots
• The instanton homology of the (-2,3,q) pretzel knots and computed bounding cochains in the pillowcase
• Knots, sutures and excision