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

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

2001-01-03

arxiv.org/abs/math/0101024v1

Trans.Am.Math.Soc. 352 (2001) 3473-3493

Mathematics

Algebraic Topology

19 pages, amstex

Scientific paper

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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