Abstract

This paper studies the covolumes of nonuniform arithmetic lattices in PU(n, 1). We determine the smallest covolume nonuniform arithmetic lattices for each n, the number of minimal covolume lattices for each n, and study the growth of the minimal covolume as n varies. In particular, there is a unique lattice (up to isomorphism) in PU(9, 1) of smallest Euler-Poincaré characteristic amongst all nonuniform arithmetic lattices in PU(n, 1). We also show that for each even n there are arbitrarily large families of nonisomorphic maximal nonuniform lattices in PU(n, 1) of equal covolume.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 143-164
Launched on MUSE
2014-01-22
Open Access
No
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