Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.
and Sisto, Alessandro , TITLE =
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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.
A group has σ-compact Morse boundary precisely when it satisfies the Morse local-to-global property, enabling construction of the first non-virtually cyclic example with an infinite-order Morse element outside acylindrical hyperbolicity.
Under geometric branching conditions, quasiisometric embeddings of CAT(0) cube complexes map flats to near-flats, inducing embeddings on Tits boundary graphs.
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic under orientability conditions on JSJ decompositions, via bounded central extensions of orbifold mapping class groups, with a sharpness counterexample.
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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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Connections between the topology of the Morse boundary, the Morse local-to-global property and acylindrical hyperbolicity
A group has σ-compact Morse boundary precisely when it satisfies the Morse local-to-global property, enabling construction of the first non-virtually cyclic example with an infinite-order Morse element outside acylindrical hyperbolicity.
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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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Outer automorphism groups of hyperbolic groups, bounded extensions, and hierarchical hyperbolicity
Outer automorphism groups of one-ended hyperbolic groups are virtually hierarchically hyperbolic under orientability conditions on JSJ decompositions, via bounded central extensions of orbifold mapping class groups, with a sharpness counterexample.