Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces

Details Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces

2007-05-20

arxiv.org/abs/0705.2891v7

Publ. Math. IHES 109(2009)

Mathematics

Differential Geometry

62 pages

Scientific paper

10.1007/s10240-009-0019-6

We introduce the notion of weak commensurabilty of arithmetic subgroups and
relate it to the length equivalence and isospectrality of locally symmetric
spaces. We prove many strong consequences of weak commensurabilty and derive
from these many interesting results about isolength and isospectral locally
symmetric spaces.

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