Morse Homology for the Yang-Mills Gradient Flow

Mathematics – Differential Geometry

Scientific paper

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71 pages

Scientific paper

We use the Yang-Mills gradient flow on the space of connections over a closed
Riemann surface to construct a Morse-Bott chain complex. The chain groups are
generated by Yang-Mills connections. The boundary operator is defined by
counting the elements of appropriately defined moduli spaces of Yang-Mills
gradient flow lines that converge asymptotically to Yang-Mills connections.

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