Toledo invariant of lattices in SU(2,1) via symmetric square

Abstract

In this paper, we address the issue of quaternionic Toledo invariant to study the character variety of two dimensional complex hyperbolic uniform lattices into $SU(n,2)$. We construct four distinct representations to prove that the character variety contains at least four distinct components. We also address the existence of holomorphic horizontal lift to various period domains of $SU(n,2)$.

23 pages, Expanded and added some materials, corrected Lemma 3.2

References in corpus (2)

• Maximal representations of complex hyperbolic lattices in SU(m,n)
• A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space