2008-04-04

Tyakal Venkataramana, Cornell University

Lefschetz type results for certain hyperbolic manifolds

We show that (Hecke translates of) low degree cohomology classes on a compact complex hyperbolic manifold restrict non-trivially to any complex submanifold, provided its fundamental group is an arithmetic group. Conjectures which say that a simlar statement is true for real hyperbolic manifolds will also be reviewed.