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- W2409168509 abstract "We study unimodular measures on the space $mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups of Lie groups. Unimodularity is preserved under weak* limits, and under certain geometric constraints (e.g. bounded geometry) unimodular measures can be used to compactify sets of finite volume manifolds. One can then understand the geometry of manifolds $M$ with large, finite volume by passing to unimodular limits. We develop a structure theory for unimodular measures on $mathcal M^d$, characterizing them via invariance under a certain geodesic flow, and showing that they correspond to transverse measures on a foliated `desingularization' of $mathcal M^d$. We also give a geometric proof of a compactness theorem for unimodular measures on the space of pointed manifolds with pinched negative curvature, and characterize unimodular measures supported on hyperbolic $3$-manifolds with finitely generated fundamental group." @default.
- W2409168509 created "2016-06-24" @default.
- W2409168509 creator A5011226645 @default.
- W2409168509 creator A5090415354 @default.
- W2409168509 date "2022-12-12" @default.
- W2409168509 modified "2023-10-03" @default.
- W2409168509 title "Unimodular measures on the space of all Riemannian manifolds" @default.
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- W2409168509 doi "https://doi.org/10.2140/gt.2022.26.2295" @default.
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