The symplectic Floer homology of the figure eight knot (Q5929563)

In a previous paper [J. Knot Theory Ramifications 6, 851-877 (1997; Zbl 0901.57003)], the author generalized the Casson-Lin invariant [see for example \textit{X. S. Lin}, J. Differ. Geom. 35, 337-357 (1992; Zbl 0774.57007)] to the symplectic theory point of view. This permits to define the symplectic Floer homology of knots. The paper is devoted to compute explicitly the symplectic Floer homology \(HF^{sym}_i\) of the figure-eight knot \(4_1\). The main result states that this homology is trivial in all degrees. This gives the first nontrivial knot with trivial symplectic Floer homology.