Higgs bundles for the non-compact dual of the special orthogonal group

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Bradlow, SB (Author) Other; Garcia Prada, O (Author) Other; Gothen, PB (Author) FCUP

Journal

Title: Geometriae Dedicata

Vol. 175

Pages: 1-48

ISSN: 0046-5755

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 11 Citations

Other information

Authenticus ID: P-00A-9V0

DOI: 10.1007/s10711-014-0026-8

Abstract (EN): Higgs bundles over a closed orientable surface can be defined for any real reductive Lie group . In this paper we examine the case . 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).

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 48