Weakly commensurable groups, with applications to differential geometry

Abstract

The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic groups. We have included a discussion of very recent results and conjectures on absolutely almost simple algebraic groups having the same maximal tori and finite-dimensional division algebras having the same maximal subfields.

Improved exposition, updated bibliography. arXiv admin note: substantial text overlap with arXiv:1212.1217

References in corpus (3)

• Weakly commensurable arithmetic groups, lengths of closed geodesics and isospectral locally symmetric spaces
• Weakly commensurable S-arithmetic subgroups in almost simple algebraic groups of types B and C
• Embedding functors and their arithmetic properties