Morse Homology for the Yang-Mills Gradient Flow

Abstract

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.

83 pages

References in corpus (4)

• Quantum Structures for Lagrangian Submanifolds
• Perturbed closed geodesics are periodic orbits: Index and Transversality
• A Compactness Theorem for Invariant Connections
• $L^2$-topology and Lagrangians in the space of connections over a Riemann surface