Structural properties of close II${}_1$ factors

Abstract

We show that a number of key structural properties transfer between sufficiently close II${}_1$ factors, including solidity, strong solidity, uniqueness of Cartan masas and property $\Gamma$. We also examine II${}_1$ factors close to tensor product factors, showing that such factors also factorise as a tensor product in a fashion close to the original.

Minor typos corrected. Munster J. Math., to appear. 16 pages, section 2 contains material from arXiv:1209.4116v2 which was removed from the final published version (v3)