Mathematics – Geometric Topology
Scientific paper
2008-06-18
Mathematics
Geometric Topology
78 pages, 15 figures. Version 3: Rearrangement of sections on the Chern class. A theorem on monotonicity of the extended modul
Scientific paper
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 ${\mathscr M}$ with an action of the braid group $B_{2n}$ preserving the symplectic structure. The action allows to associate a Lagrangian submanifold of ${\mathscr M}$ 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. We expect this to go some way in explaining the similarities mentioned above.
Jacobsson Magnus
Rubinsztein Ryszard L.
No associations
LandOfFree
Symplectic topology of SU(2)-representation varieties and link homology, I: Symplectic braid action and the first Chern class does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Symplectic topology of SU(2)-representation varieties and link homology, I: Symplectic braid action and the first Chern class, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Symplectic topology of SU(2)-representation varieties and link homology, I: Symplectic braid action and the first Chern class will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-272077