Variations of Thompson's Group F and Subdivisions
by
Sean Cleary
California State University, Fresno

Thompson's group F of PL homeomorphisms with dyadic breakpoints and slopes which are powers of two has variations to other possible breakpoint rings and slope groups. Subdivision techniques for these one-dimensional sets which are straightforward in the rational case can become interesting in some irrational cases. I discuss general strategies for subdivision in these cases, which can be used to show finiteness properties for the groups. I develop connections with one-dimensional aperiodic tilings and some simple substitution tilings, and discuss some other number-theortic inspired variations of Thompson's group F.

Date received: April 15, 1998

Copyright © 1998 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 # cabb-20.