On the symmetric span of solenoids
by
Raúl Escobedo
Benemérita Universidad Autónoma de Puebla

Let p = p₁, p₂, ... be a sequence of positive integers. The p-adic solenoid, S_p, is defined as the inverse limit of unit circles X_n = S¹ = { z in C | |z|=1 } where the bonding maps f_n : X_n+1 --> X_n are given by the formula f_n(z) = z^p_n.

H. Cook, essentially proved that the symmetric span of the dyadic solenoid (p_n=2 for each n) is zero, but he never published that result.

K. Kawamura proved a more general result: The symmetric span of S_p is positive if and only if there exists a positive integer N such that for every n >= N, p_n is odd.

We will give a different proof of the following fact: If p = p₁, p₂, ... has a subsequence of even numbers, then the symmetric span of S_p is zero.

We will also show that every topological group has positive span.

Date received: March 17, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caal-03.