uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Symplectic topology of SU(2)-representation varieties and link homology, I: Symplectic braid action and the first Chern class
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. (Algebra, Geometry and Logic)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

Keyword [en]
Topology of SU(2)-representation varieties, symplectic structure invariant under a braid group action, its Lagrangian submanifolds, its almost complex structure.
National Category
Research subject
URN: urn:nbn:se:uu:diva-105809OAI: oai:DiVA.org:uu-105809DiVA: diva2:222546
Topological quandles and link homology
Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2010-01-14

Open Access in DiVA

No full text

By organisation
Department of Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 184 hits
ReferencesLink to record
Permanent link

Direct link