What question did this study set out to answer?

To examine the Yang-Mills functional on compact Riemann surfaces via Morse theory and determine the topological structure of the moduli space of algebraic vector bundles.

March 17, 1983Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences

The Yang-Mills equations over Riemann surfaces

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Authors

MAMichael AtiyahAl-Muthanna University RBRaoul BottDePaul University

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Implication

Theoretical analysis reveals a perfect Yang-Mills functional over Riemann surfaces, highlighting the topological structure of moduli spaces of algebraic bundles.

Key Points

To examine the Yang-Mills functional on compact Riemann surfaces via Morse theory and determine the topological structure of the moduli space of algebraic vector bundles.
Formulated an equivariant Morse theory framework tailored to account for infinite-dimensional gauge symmetry.
Analyzed the geometric relationship and interplay between holomorphic bundle structures and unitary connections over Riemann surfaces.
Demonstrated that the gauge-equivariant Yang-Mills functional satisfies the criteria of a perfect Morse functional.
Derived topological invariants and cohomology determinations for the critical sets and the moduli space of stable algebraic bundles.

Cite This Study

Atiyah et al. (1983) studied this question.

synapsesocial.com/papers/6a01c4dc0ed7d2e5335c99b4 https://doi.org/10.1098/rsta.1983.0017

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Implication

Theoretical analysis reveals a perfect Yang-Mills functional over Riemann surfaces, highlighting the topological structure of moduli spaces of algebraic bundles.

The Yang-Mills equations over Riemann surfaces

Discussion

Member takes

Implication

Key Points

Cite This Study

The Yang-Mills equations over Riemann surfaces

Discussion

Member takes

Implication

Key Points

Cite This Study

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