Exponents and Bundles over Tori
by
Alex Clark
University of North Texas

Given a map of a contractible subspace of a Euclidean space into a metric space, we introduce its exponent group - an associated group of matrices. We explore the topological significance of this group. In particular, under certain conditions their is a natural fiber bundle over a torus of the same dimension as the domain of the map, and the structure of the bundle is related with the exponent group of the map. Given any countable subgroup of the reals, we show how to obtain a one-dimensional compact minimal set for a flow which has this group as its exponent group. The analogue in higher dimensions is discussed.

Date received: February 14, 2000

Copyright © 2000 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 Mathematical Conference Abstracts. Document # cady-54.