Complete characterization of quasiisometric embeddings between RAAGs on cycle graphs, including exotic cases without subgroup relations and hyperbolic plane embeddings into certain RAAGs.
Eu- ropean Mathematical Society (EMS), Z¨ urich, 2016, pp
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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.
Under geometric branching conditions, quasiisometric embeddings of CAT(0) cube complexes map flats to near-flats, inducing embeddings on Tits boundary graphs.
Introduces generalisable presentations and topological RAAGs as locally compact groups, studies their Salvetti-type complexes, and constructs TDLC examples of type FP_n but not FP_{n+1}.
Describes Higson corona via coarse ultrafilter quotients to prove faithfulness of corona functor, gives Künneth formula for twisted coarse cohomology, and obtains Gromov boundary as quotient of Higson corona.
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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.
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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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Generalisable presentations and compactness properties of locally compact right-angled Artin groups
Introduces generalisable presentations and topological RAAGs as locally compact groups, studies their Salvetti-type complexes, and constructs TDLC examples of type FP_n but not FP_{n+1}.
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Coarse Homotopy on metric Spaces and their Corona
Describes Higson corona via coarse ultrafilter quotients to prove faithfulness of corona functor, gives Künneth formula for twisted coarse cohomology, and obtains Gromov boundary as quotient of Higson corona.