9,649 research outputs found
Asymptotic Dimension
The asymptotic dimension theory was founded by Gromov in the early 90s. In
this paper we give a survey of its recent history where we emphasize two of its
features: an analogy with the dimension theory of compact metric spaces and
applications to the theory of discrete groups.Comment: Added some remarks about coarse equivalence of finitely generated
groups
On G-sets and Isospectrality
We study finite G-sets and their tensor product with Riemannian manifolds,
and obtain results on isospectral quotients and covers. In particular, we show
the following: if M is a compact connected Riemannian manifold (or orbifold)
whose fundamental group has a finite non-cyclic quotient, then M has
isospectral non-isometric covers
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