Casson-Lin's invariant of a knot and Floer homology
| dc.creator | Li, Weiping | |
| dc.date | 1996-05-22 | |
| dc.date.accessioned | 2026-07-07T09:16:59Z | |
| dc.date.available | 2026-07-07T09:16:59Z | |
| dc.description | A. Casson defined an intersection number invariant which can be roughly thought of as the number of conjugacy classes of irreducible representations of $π_1(Y)$ 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 $S^3$. 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 $π_1(S^3 \setminus K)$ 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. | |
| dc.description | 22 pages, AmsLaTex | |
| dc.identifier | https://arxiv.org/abs/q-alg/9605036 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9605036 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153549 | |
| dc.subject | Quantum Algebra | |
| dc.title | Casson-Lin's invariant of a knot and Floer homology | |
| dc.type | text |