Rank-2 Kleinian groups with three parabolics are maximal cusps when the domain of discontinuity is nonempty, but new finite-covolume lattice examples exist that do not arise from tunnel-number-1 links.
and Canary, Richard D
5 Pith papers cite this work, alongside 264 external citations. Polarity classification is still indexing.
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Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.
Branching conditions on RAAG defining graphs force quasiisometric embeddings to induce extension graph embeddings, enabling rigidity theorems including obstructions to tree-product embeddings, classifications for cycle RAAGs, and non-universal receivers in each dimension.
Under geometric branching conditions, quasiisometric embeddings of CAT(0) cube complexes map flats to near-flats, inducing embeddings on Tits boundary graphs.
A survey organizing known results on the dynamics of mapping class group actions on character varieties of surface groups, emphasizing the compact-versus-non-compact dichotomy and covering PSL(2,R), compact groups, PSL(2,C), and higher-rank Lie groups.
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On rank two Kleinian groups with three parabolics
Rank-2 Kleinian groups with three parabolics are maximal cusps when the domain of discontinuity is nonempty, but new finite-covolume lattice examples exist that do not arise from tunnel-number-1 links.
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Quasiisometric embeddings between right-angled Artin groups: flexibility
Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.
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Quasiisometric embeddings between right-angled Artin groups: rigidity
Branching conditions on RAAG defining graphs force quasiisometric embeddings to induce extension graph embeddings, enabling rigidity theorems including obstructions to tree-product embeddings, classifications for cycle RAAGs, and non-universal receivers in each dimension.
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From branching quasiflats to flats in CAT(0) cube complexes
Under geometric branching conditions, quasiisometric embeddings of CAT(0) cube complexes map flats to near-flats, inducing embeddings on Tits boundary graphs.
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Dynamics and geometry of character varieties for surface groups
A survey organizing known results on the dynamics of mapping class group actions on character varieties of surface groups, emphasizing the compact-versus-non-compact dichotomy and covering PSL(2,R), compact groups, PSL(2,C), and higher-rank Lie groups.