Symplectic topology of SU(2)-representation varieties and link homology, I: Symplectic braid action and the first Chern class
(English)Manuscript (preprint) (Other academic)
There are some similarities between cohomology of SU(2)-representation varieties of the fundamental group of some link complements and the Khovanov homology of the links. We start here a program to explain a possible source of these similarities. We introduce a symplectic manifold M with an action of the braid group B(2n) preserving the symplectic structure. The action allows to associate a Lagrangian submanifold of M to every braid. The representation variety of a link can then be described as the intersection of such Lagrangian submanifolds, given a braid presentation of the link. In a sequel to this paper we shall refine representation varieties of links using this description. We expect this to go some way in explaining the similarities mentioned above.
Topology of SU(2)-representation varieties, symplectic structure invariant under a braid group action, its Lagrangian submanifolds, its almost complex structure.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:uu:diva-105809OAI: oai:DiVA.org:uu-105809DiVA: diva2:222546
ProjectsTopological quandles and link homology