Continua that admit expansive Zⁿ⁺¹ actions but do not admit expansive Zⁿ actions.
by
Christopher G. Mouron
Rhodes College

A collection of commuting automorphisms {f₁, ..., f_n} on a continuum X is an expansive Zⁿ action provided that for some fixed c > 0 and every x, y ∈ X there exists (r₁, ..., r_n) ∈ Zⁿ such that d(f₁^r₁○f₂^r₂○...f_n^r_n(x), f₁^r₁○f₂^r₂○...f_n^r_n(y)) > c. Expansive homeomorphisms are expansive Z¹ actions. In this talk, I will show that for any pair of natural numbers k and n there exists a k-dimensional continuum that admits an expansive Zⁿ⁺¹ action but does not admit an expansive Zⁿ action.

Date received: February 28, 2006