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

We define an elementary relatively 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.


Publication Date:
2018
Date Submitted:
Nov 21 2018
ISSN:
1527-5256
Citation:
Journal of Symplectic Geometry
Note:
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 Record created 2018-11-21, last modified 2019-04-03


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