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Introduction to Nonabelian Hodge Theory

Flat connections, Higgs bundles and complex variations of Hodge structure
  • Alberto García-RabosoEmail author
  • Steven RayanEmail author
Chapter
Part of the Fields Institute Monographs book series (FIM, volume 34)

Abstract

Hodge theory bridges the topological, smooth and holomorphic worlds. In the abelian case of the preceding chapter, these are embodied by the Betti, de Rham and Dolbeault cohomology groups, respectively, of a smooth compact Kähler manifold, X.

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Notes

Acknowledgements

We thank Chuck Doran, David Morrison, Radu Laza, and Johannes Walcher for organizing the Workshop on Hodge Theory in String Theory, as well as Alan Thompson for arranging the concentrated graduate course in which we gave these lectures. We are indebted to Noriko Yui for encouraging us to contribute these notes, and for organizing a vibrant and productive thematic program at the Fields Institute. These notes benefited from useful comments and suggestions by Philip Boalch, Tamás Hausel, Tony Pantev, and an anonymous referee. We also thank Marco Gualtieri and Lisa Jeffrey for their support and for providing a stimulating working environment in Toronto.

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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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