Year: 2006
Type: preprint
Abstract: We show that if n>5, PU(n-1,1) does not contain a cocompact arithmetic subgroup with the same Euler-Poincare characteristic (in the sense of C.T.C. Wall) as the complex projective space of dimension n-1, and show that if n=5, there are at least four such subgroups, which are in fact torsion-free. This, in particular, leads to examples of a fake projective space of dimension 4. Analogous results for arithmetic fake grassmannians Gr(m,n) with n>3 odd are also obtained.
Source: arXiv (Cornell University)
Authors: Prasad, Gopal, Yeung, Sai-Kee
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952795351