1996/05/22 by Wei-Ping Li, Li, Weiping
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.q-alg/9605036
openalex publication_date 1996/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A. Casson defined an intersection number invariant which can be roughly thought of as the number of conjugacy classes of irreducible representations of π1(Y) into SU(2) counted with signs, where Y is an oriented integral homology 3-sphere. X.S. Lin defined an similar invariant (signature of a knot) to a braid representative of a knot in S3. In this paper, we give a natural generalization of the Casson-Lin's invariant to be (instead of using the instanton Floer homology) the symplectic Floer homology for the representation space (one singular point) of π1(S3 ∖ K) into SU(2) with trace-free along all meridians. The symplectic Floer homology of braids is a new invariant of knots and its Euler number of such a symplectic Floer homology is the negative of the Casson-Lin's invariant.