38 research outputs found
Arithmetic fake projective spaces and arithmetic fake grassmannians
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.Comment: 20 pages, the exposition has been improve
Nonexistence of arithmetic fake compact hermitian symmetric spaces of types other than An
We show that there are no arithmetic fake compact hermitian symmetric spaces
of type other than An for n>4.Comment: 38 pages, an expanded and improved version of the original article to
include consideration of type An for n>4, to appear in Journal of
Mathematical Society of Japa