TY - JOUR
T1 - SO (p, q) -Higgs bundles and Higher Teichmüller components
AU - Aparicio-Arroyo, Marta
AU - Bradlow, Steven
AU - Collier, Brian
AU - García-Prada, Oscar
AU - Gothen, Peter B.
AU - Oliveira, André
N1 - The authors acknowledge support from U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 \u201CRNMS: GEometric structures And Representation varieties\u201D (the GEAR Network). The third author is funded by a National Science Foundation Mathematical Sciences Postdoctoral Fellowship, NSF MSPRF no. 1604263. The fourth author was partially supported by the Spanish MINECO under ICMAT Severo Ochoa Project No. SEV-2015-0554, and under Grant No. MTM2016-81048-P. The fifth and sixth authors were partially supported by CMUP (UID/MAT/00144/2019) and the Project PTDC/MAT-GEO/2823/2014 funded by FCT (Portugal) with national funds. The sixth author was also partially supported by the Post-Doctoral fellowship SFRH/BPD/100996/2014 funded by FCT (Portugal) with national funds.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such ‘exotic’ components in moduli spaces of SO (p, q) -Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO (p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO (2 , q) , with q⩾ 4).
AB - Some connected components of a moduli space are mundane in the sense that they are distinguished only by obvious topological invariants or have no special characteristics. Others are more alluring and unusual either because they are not detected by primary invariants, or because they have special geometric significance, or both. In this paper we describe new examples of such ‘exotic’ components in moduli spaces of SO (p, q) -Higgs bundles on closed Riemann surfaces or, equivalently, moduli spaces of surface group representations into the Lie group SO (p, q). Furthermore, we discuss how these exotic components are related to the notion of positive Anosov representations recently developed by Guichard and Wienhard. We also provide a complete count of the connected components of these moduli spaces (except for SO (2 , q) , with q⩾ 4).
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U2 - 10.1007/s00222-019-00885-2
DO - 10.1007/s00222-019-00885-2
M3 - Article
AN - SCOPUS:85068852833
SN - 0020-9910
VL - 218
SP - 197
EP - 299
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -