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Scientific article
Open access
English

Arbitrarily large families of spaces of the same volume

ContributorsEmery, Vincent
Published inGeometriae Dedicata, vol. 160, no. 1, p. 313-320
Collection
  • Open Access - Licence nationale Springer 
Publication date2012
Abstract

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL2(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.

Citation (ISO format)
EMERY, Vincent. Arbitrarily large families of spaces of the same volume. In: Geometriae Dedicata, 2012, vol. 160, n° 1, p. 313–320. doi: 10.1007/s10711-011-9684-y
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Article (Published version)
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ISSN of the journal1572-9168
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