Arithmetic fake projective spaces and arithmetic fake grassmannians

Details Arithmetic fake projective spaces and arithmetic fake grassmannians Arithmetic fake projective spaces and arithmetic fake grassmannians

2006-02-07

arxiv.org/abs/math/0602144v4

Mathematics

Algebraic Geometry

20 pages, the exposition has been improved

Scientific paper

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.

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