Corpus ID: 119605037

Surface group representations, Higgs bundles, and holomorphic triples

@inproceedings{Bradlow2002SurfaceGR,
  title={Surface group representations, Higgs bundles, and holomorphic triples},
  author={Steven B. Bradlow and Oscar Garc{\'i}a-Prada and Peter B. Gothen},
  year={2002}
}
Using the $L^2$ norm of the Higgs field as a Morse function, we study the moduli spaces of $U(p,q)$-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on $(p,q)$. A key step is the identification of the function's local minima as moduli spaces of holomorphic triples. We prove that these moduli spaces of triples are irreducible and non-empty. Because of the relation between flat bundles and fundamental group representations… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 36 REFERENCES

The moduli of flat PU(2, 1) structures over Riemann surfaces

  • E. Z. Xia
  • Pacific Journal of Mathematics 195,
  • 2000
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

Lie groups and teichmüller space

VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

Flat $G$-bundles with canonical metrics

VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL