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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.05179 |
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Table of Contents:
- In this paper, we show that for a graph $Γ$ from a class named H-rigid graphs, its subgraph ${\rm Int}(Γ)$, named the internal graph of $Γ$, is an isomorphism invariant of the graph product of hyperfinite II$_1$-factors $R_Γ$. In particular, we can classify $R_Γ$ for some typical types of graphs, such as lines, cyclic graphs and infinite regular trees. As an application, we also show that for two isomorphic graph products of hyperfinite II$_1$-factors over H-rigid graphs, the difference of the radius between the two graphs will not be larger than 1. Our proof is based on the recent resolution of the Peterson-Thom conjecture.