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3-handle construction on II$_1$ factors

David Gao, Srivatsav Kunnawalkam Elayavalli, Gregory Patchell

Abstract

We find a subtle modification to the construction of Chifan-Ioana-Kunnawalkam Elayavalli, which yields a drastic simplification of the proof of the existence of two non Gamma non elementarily equivalent II$_1$ factors.

3-handle construction on II$_1$ factors

Abstract

We find a subtle modification to the construction of Chifan-Ioana-Kunnawalkam Elayavalli, which yields a drastic simplification of the proof of the existence of two non Gamma non elementarily equivalent II factors.

Paper Structure

This paper contains 3 sections, 1 theorem, 1 equation.

Table of Contents

  1. The construction
  2. Showing that $M$ is a non Gamma II$_1$ factor
  3. Proving non elementary equivalence

Key Result

Theorem A

For any ultrafilters $\mathcal{U},\mathcal{V}$ on sets $I, J$ respectively, $M^\mathcal{U}\ncong L(\mathbb{F}_2)^\mathcal{V}$. Moreover $3\leq \mathfrak{D}(M)\leq 4$ where $\mathfrak{D}(M)$ denotes the commutation diameter introduced in elayavalli2023sequential.

Theorems & Definitions (1)

  • Theorem A