Rank one Higgs bundles and representations of fundamental groups of Riemann surfaces /
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| Author / Creator: | Goldman, William Mark. |
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| Imprint: | Providence, R.I. : American Mathematical Society, c2008. |
| Description: | vii, 69 p. ; 26 cm. |
| Language: | English |
| Series: | Memoirs of the American Mathematical Society, 0065-9266 ; no. 904 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6832094 |
| Summary: | 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 $X$. |
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| Item Description: | "May 2008, volume 193, number 904 (fourth of 5 numbers)." |
| Physical Description: | vii, 69 p. ; 26 cm. |
| Bibliography: | Includes bibliographical references (p. 67-69). |
| ISBN: | 9780821841365 082184136X |
