Twisted Tensor Products
by
S. Silberger
Hofstra University
Coauthors: H.M. Hastings, M.T. Weiss, Y. Wu

By subshift of finite type we mean subshift of finite type which are represented by a matrix. It is easy to see that the product of two subshifts of finite type can be represented by the tensor product of the matrices. The Williams conjecture proposes that two subshifts of finite type are topologically conjugate if their matrices are shift equivalent. The Ashley example is a subshift of finite type that is shift equivalent to the full two-shift. It is unknown whether it is, in fact, conjugate to the full two shift and therefore has been studied as a possible counter-example to the Williams conjecter. Recently, H. Kim and F. W. Roush disproved the Williams conjecture with an entirely different set of subshifts. However, it has never been decided if the Ashley example is indeed another counter-example. In analogy with the definition of fibre bundles as twisted products, we defined twisted tensor products and recognized that the Ashley example can be represented by a twisted tensor product over the full two-shift. This talk is on our preliminary results about twisted tensor products.

Date received: July 24, 1999

Copyright © 1999 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 # cacl-99.