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

2001/01/03 by U. Gritsch
Mathematics · #math.AT #msc:58E15 #msc:55P91

paper · pdf

published as Trans.Am.Math.Soc. 352 (2001) 3473-3493 · 19 pages, amstex

arxiv created 2001/01/03 · arxiv updated 2009/11/30

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 with generic SU(2)-invariant metrics using Morse and homotopy theoretic methods. These manifolds are acted on fixed point freely by the Lie group 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 and by Rade.

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• The Yang-Mills measure on surfaces via Morse theory
• Morse index stability for p-Yang-Mills connections
• Elliptic Yang-Mills Flow Theory
• Morse theory and stable pairs
• The Variations of Yang-Mills Lagrangian