SL(2,C) Floer cohomology for surgeries on some knots
Abstract
We establish a relationship between the sheaf-theoretic SL(2,C) Floer cohomology HP(Y), as defined by Abouzaid and Manolescu, for Y a surgery on a small knot in S3, and the SL(2,C) Casson invariant, as defined by Curtis. We determine a similar formula involving the framed sheaf-theoretic SL(2,C) Floer cohomology, HP#(Y). We use these relationships to compute HP and HP# for most surgeries on two-bridge knots. We also compute HP for surgeries on two non-small knots, the granny and square knots.
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