Topological invariants of Anosov representations

• Verfasst von: Guichard, Olivier [VerfasserIn]
• Verfasst von: Wienhard, Anna [VerfasserIn]
• Titel: Topological invariants of Anosov representations
• Verf.angabe: Guichard Olivier and Wienhard Anna
• Umfang: 65 S.
• Fussnoten: Gesehen am 18.04.2018
• Titel Quelle: Enthalten in: Journal of topology
• Jahr Quelle: 2010
• Band/Heft Quelle: 3(2010), 3, S. 578-642
• ISSN Quelle: 1753-8424
• DOI: doi:10.1112/jtopol/jtq018
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1572134674

Abstract

We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface Σ into the symplectic group Sp (2n, R). In particular we show that the invariants distinguish connected components of the space of symplectic maximal representations other than Hitchin components. Since the invariants behave naturally with respect to the action of the mapping class group of Σ, we obtain from this the number of components of the quotient by the mapping class group action. For specific symplectic maximal representations we compute the invariants explicitly. This allows us to construct nice model representations in all connected components. The construction of model representations is of particular interest for Sp (4, R), because in this case there are ?1??(Σ) connected components in which all representations are Zariski dense and no model representations have been known so far. Finally, we use the model representations to draw conclusions about the holonomy of symplectic maximal representations.