# David Auckly
Kansas State University

## Topology of a non linear sigma model

The Skyrme model was developed as a nonlinear theory of
pions.
Since the analytical behavior of the Skyrme model is not well
understood,
and since there is not much experimental data to test the Skyrme
model,
various modifications of the Skyrme model are studied. One such
modification was proposed by L. Faddeev. This model is described
by a functional for maps from a 3-manifold into a 2-sphere. Numerical
studies indicate that this model should produce interesting knotted
solitons, but very little is known about this functional. In this
talk,
we will describe work in progress (joint with L. Kapitanski) aimed
at proving that there is a mimimizer of the Faddeev functional in
each
homotopy class of maps.