Arbitrarily large families of spaces of the same volume

作者：Emery Vincent^*

来源：Geometriae Dedicata, 2012, 160(1): 313-320.

DOI：10.1007/s10711-011-9684-y

• Locally symmetric spaces
• Arithmetic lattices
• Volume

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

• 出版日期2012-10