Khovanov Homology And Gauge Theory

Details Khovanov Homology And Gauge Theory Khovanov Homology And Gauge Theory

2011-08-15

arxiv.org/abs/1108.3103v1

Mathematics

Geometric Topology

16 pp

Scientific paper

In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and five-dimensional manifolds with boundary, with a rather subtle boundary condition that encodes the knots and links. The construction is formally analogous to Floer and Donaldson theory in three and four dimensions. It was discovered using quantum field theory arguments but can be described and understood purely in terms of classical gauge theory. (Based on a lecture at the conference Low-Dimensional Manifolds and High-Dimensional Categories, University of California at Berkeley, June 2011).

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