On Matoušek-like Embedding Obstructions of Countably Branching Graphs

Abstract

In this paper we present new proofs of the non-embeddability of countably branching trees into Banach spaces satisfying property $({\beta }_p)$ and of countably branching diamonds into Banach spaces which are $p$-AMUC for $p>1$. These proofs are entirely metric in nature and are inspired by previous work of Jiří Matoušek. In addition, using this metric method, we succeed in extending these results to metric spaces satisfying certain curvature-like inequalities. Finally, we extend an embedding result of Tessera to give lower bounds on the compression for a class of Lipschitz embeddings of the countably branching trees into Banach spaces containing ${\ell }_p$-asymptotic models for $p\ge 1$.

28 pages, 3 figures; expanded out author names in references instead of using et al

References in corpus (3)

• On the geometry of the countably branching diamond graphs
• $(\beta )$-distortion of some infinite graphs
• A coding of bundle graphs and their embeddings into Banach spaces