Knot homology groups from instantons

For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology.

Bibliographic Details
Main Authors: Kronheimer, P. B., Mrowka, Tomasz S.
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:en_US
Published: Oxford University Press - London Mathematical Society 2015
Online Access:http://hdl.handle.net/1721.1/93165
https://orcid.org/0000-0001-9520-6535
Description
Summary:For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology.