RANK ONE HIGGS BUNDLES AND REPRESENTATIONS OF FUNDAMENTAL GROUPS OF RIEMANN SURFACES by William M. Goldman, Eugene Z. Xia ( 9780821841365 )

Item Details

Title:

RANK ONE HIGGS BUNDLES AND REPRESENTATIONS OF FUNDAMENTAL GROUPS OF RIEMANN SURFACES

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Format:

Paperback

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ISBN 10:

082184136X

ISBN 13:

9780821841365

Publisher:

AMERICAN MATHEMATICAL SOCIETY

Pub. date:

15 April, 2008

Series:

Memoirs of the American Mathematical Society 193, 904

Pages:

Description:

Details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. This work constructs an equivalence between the deformation theories of flat connections and Higgs pairs, providing an identification of moduli spaces arising in different contexts.

Synopsis:

This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkahler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.

Publication:

Imprint:

American Mathematical Society

Returns:

Returnable

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