Strong Shift Equivalence Theory
by
J.B. Wagoner
UC Berkeley

This talk lays the ground work for Kim's talk on the Kim-Roush counterexample to Williams Conjecture which says that shift equivalence implies strong shift equivalence for primitive matrices. We discuss the spaces RS(Z) and RS(Z⁺) of strong shift equivalences over the integers Z and the nonnegative integers Z⁺. We discuss how this leads to a general program for finding counterexamples to Williams Conjecture that brings in relative 1-cocyles on the pair of spaces (RS(Z), X) where X is the union of certain components of RS(Z⁺) This strategy was discovered independently by Kim and Roush. Kim will then describe how to construct a counterexample using a 1-cocycle coming from the sign-gyration-compatibilty-condition homomorphism.

Date received: February 23, 1998