A family of non-isomorphism results
Skip to main content
eScholarship
Open Access Publications from the University of California

A family of non-isomorphism results

  • Author(s): Bleak, Collin
  • Lanoue, Daniel
  • et al.
Abstract

We calculate the local groups of germs associated with the higher dimensional R. Thompson groups nV. For a given $${n\in N\cup\left\{\omega\right\}}$$ , these groups of germs are free abelian groups of rank r, for r ≤ n (there are some groups of germs associated with nV with rank precisely k for each index 1 ≤ k ≤ n). By Rubin’s theorem, any conjectured isomorphism between higher dimensional R. Thompson groups induces an isomorphism between associated groups of germs. Thus, if m ≠ n the groups mV and nV cannot be isomorphic. This answers a question of Brin.

Many UC-authored scholarly publications are freely available on this site because of the UC Academic Senate's Open Access Policy. Let us know how this access is important for you.

Main Content
Current View