Quasi-actions on trees I. Bounded valence
Given a bounded valence, bushy tree $T$, we prove that any cobounded quasi-action of a group $G$ on $T$ is quasiconjugate to an action of $G$ on another bounded valence, bushy tree $T’$. This theorem...
View ArticleGroups acting properly on “bolic” spaces and the Novikov conjecture
We introduce a class of metric spaces which we call “bolic”. They include hyperbolic spaces, simply connected complete manifolds of nonpositive curvature, euclidean buildings, etc. We prove the Novikov...
View ArticleSum rules for Jacobi matrices and their applications to spectral theory
We discuss the proof of and systematic application of Case’s sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among...
View ArticleFundamental groups of manifolds with positive isotropic curvature
A central theme in Riemannian geometry is understanding the relationships between the curvature and the topology of a Riemannian manifold. Positive isotropic curvature (PIC) is a natural and much...
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