English

Monodromy, vanishing cycles, knots and the adjoint quotient

Symplectic Geometry 2007-05-23 v1 Geometric Topology

Abstract

These are notes from lectures given at the Clay Institute Summer School on "Floer homology, gauge theory and low-dimensional topology" (Budapest, 2004). The first part describes as background some of the geometry of symplectic fibre bundles and their monodromy. The second part, overviewing joint work with Paul Seidel, applies these general ideas and Floer cohomology to certain fibre bundles that arise naturally in Lie theory. This constructs an invariant of oriented links in the three-sphere which is conjecturally equal to Khovanov's combinatorial homology theory.

Keywords

Cite

@article{arxiv.math/0412440,
  title  = {Monodromy, vanishing cycles, knots and the adjoint quotient},
  author = {Ivan Smith},
  journal= {arXiv preprint arXiv:math/0412440},
  year   = {2007}
}

Comments

20 pages, 5 figures. Clay Institute lectures