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arXiv · 1107.3043

Arbitrarily large families of spaces of the same volume

Vincent Emery
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Abstract

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.

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Vincent Emery. 2011-07-15. Arbitrarily large families of spaces of the same volume. https://doi.org/10.1007/s10711-011-9684-y

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