Morse theory for the Yang-Mills functional via equivariant homotopy theory

Abstract

In this paper we show the existence of non-minimal critical points of the Yang-Mills functional over a certain family of 4-manifolds{M2g:g=0,1,2,…}\{ M_{2g} : g=0,1,2, \ldots \}with genericSU(2)SU(2)-invariant metrics using Morse and homotopy theoretic methods. These manifolds are acted on fixed point freely by the Lie groupSU(2)SU(2)with quotient a compact Riemann surface of even genus. We use a version of invariant Morse theory for the Yang-Mills functional used by Parker inA Morse theory for equivariant Yang-Mills, Duke Math. J.66-2 (1992), 337–356 and Råde inCompactness theorems for invariant connections, submitted for publication.