Publication Date
Spring 2025
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
Advisor
Edgar Bering IV; Matthew Durham; Timothy Hsu
Abstract
An asymptotically CAT(0) space is one where every ball of radius r is f(r)-CAT(0) for a fixed sublinear function f. An asymptotically CAT(0) group Γ is a group which acts properly and cocompactly by isometries on an asymptotically CAT(0) space X. Fix x0 ∈ X, choose D > 0 such that X = S γ∈Γ �� γ · B �� x0, D 3 ?? , define A = {a ∈ Γ : d(x0, a · x0) ≤ D + 1}, and let R be the set of reduced words in A of length at most 10 that represent the identity in Γ. This gives Γ = ⟨A|R⟩. We prove that for any word w of length m in A which represents the identity, there exists a presentation ⟨A|R⟩ such that Am ⊆ A and the number of relations in Rm needed to express w is at most quadratic with respect to m.
Recommended Citation
Dabu, Edric D., "The Isoperimetric Inequality for Asymptotically CAT(0) Groups" (2025). Master's Theses. 5641.
DOI: https://doi.org/10.31979/etd.9ddv-4aat
https://scholarworks.sjsu.edu/etd_theses/5641
