On the Σ-invariants of generalized Thompson groups and Houghton groups

2015/02/09 by Matthew C. B. Zaremsky, Zaremsky, Matthew C. B.
Chemistry · Medicine · #20F65 #57M07 #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Infectious Diseases and Tuberculosis #Synthesis and Reactivity of Heterocycles

paper · pdf · doi:10.48550/arxiv.1502.02620

openalex publication_date 2015/02/09 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We compute the higher Σ-invariants Σ^m(F_n,∞) of the generalized Thompson groups F_n,∞, for all m,n≥ 2. This extends the n=2 case done by Bieri, Geoghegan and Kochloukova, and the m=2 case done by Kochloukova. Our approach differs from those used in the n=2 and m=2 cases; we look at the action of F_n,∞ on a \textrmCAT(0) cube complex, and use Morse theory to compute all the Σ^m(F_n,∞). We also obtain lower bounds on Σ^m(H_n), for the Houghton groups H_n, again using actions on \textrmCAT(0) cube complexes, and discuss evidence that these bounds are sharp.

Related

• The Σ-invariants of Thompson's group F via Morse theory
• The Sigma Invariants of Thompson's Group F
• Geometric structures related to the braided Thompson groups
• The Geometric Invariants of Group Extensions
• The Sigma invariants for the Golden Mean Thompson group