Counterexamples to the Williams conjecture
by
K. H. Kim
Alabama State University
Coauthors: F. W. Roush

This talk covers our recent counterexample to the irreducible case of the Williams conjecture, giving two 7x7 matrices which are shift equivalent but not strong shift equivalent, as well as our earlier 8x8 counterexample to the reducible case. It will focus on the sgcc invariants which connect the effects of automorphisms of subshifts of finite type on dimension groups to their effects on periodic points. It will not go into the semisimplicial complexes constructed by Jack Wagoner from strong shift equivalences over semirings, but will apply the results from this study to present the obstruction which enables the counterexample to be proved.

Date received: February 20, 1998