@article{bb61249cc4e14c40972f03910bb54e25,
title = "Higgs bundles for the non-compact dual of the special orthogonal group",
abstract = "Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group $$G$$G. In this paper we examine the case G=SO∗(2n). We describe a rigidity phenomenon encountered in the case of maximal Toledo invariant. Using this and Morse theory in the moduli space of Higgs bundles, we show that the moduli space is connected in this maximal Toledo case. The Morse theory also allows us to show connectedness when the Toledo invariant is zero. The correspondence between Higgs bundles and surface group representations thus allows us to count the connected components with zero and maximal Toledo invariant in the moduli space of representations of the fundamental group of the surface in SO∗(2n).",
keywords = "Higgs bundles, Moduli spaces, Real Lie groups, Surface group representations",
author = "Bradlow, {Steven B.} and Oscar Garc{\'i}a-Prada and Gothen, {Peter B.}",
note = "Funding Information: Members of the Research Group VBAC (Vector Bundles on Algebraic Curves) and the ESF Network ITGP (Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics). Second author is partially supported by the Spanish Ministerio de Ciencia e Innovaci{\'o}n (MICINN) under Grants MTM2007-67623 and MTM2010-17717. Third author partially supported by FCT (Portugal) with EU (FEDER/COMPETE) and Portuguese funds under projects PTDC/MAT/099275/2008, PTDC/MAT/098770/2008, PTDC/MAT-GEO/0675/2012 and PEst-C/MAT/UI0144/2013. The authors also acknowledge support from U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media Dordrecht.",
year = "2015",
month = apr,
day = "1",
doi = "10.1007/s10711-014-0026-8",
language = "English (US)",
volume = "175",
pages = "1--48",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer",
number = "1",
}