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- W2952285860 abstract "Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v^v such manifolds of volume at most v, considered up to commensurability. Since the number of arithmetic ones tends to be polynomial, almost all hyperbolic manifolds are non-arithmetic in an appropriate sense. Our method involves a geometric graph-of-spaces construction that relies on arithmetic properties of certain quadratic forms." @default.
- W2952285860 created "2019-06-27" @default.
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- W2952285860 date "2014-01-30" @default.
- W2952285860 modified "2023-09-23" @default.
- W2952285860 title "Counting commensurability classes of hyperbolic manifolds" @default.
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