A family of non-isomorphism results

作者：Bleak Collin^*; Lanoue Daniel

来源：Geometriae Dedicata, 2010, 146(1): 21-26.

DOI：10.1007/s10711-009-9423-9

• Higher Dimensional R. Thompson Groups nV
• Germs
• Rubin's Theorem

We calculate the local groups of germs associated with the higher dimensional R. Thompson groups nV. For a given n is an element of N boolean OR {omega}, 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 not equal n the groups mV and nV cannot be isomorphic. This answers a question of Brin.

• 出版日期2010-6