approximation_properties_summary
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approximation_properties_summary [2019/10/04 14:12] d.gromada |
approximation_properties_summary [2021/11/23 11:56] (current) |
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| ===== Mutual relationships ===== | ===== Mutual relationships ===== | ||
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| + | Residually finite ⇒ property (F) | ||
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| + | Amenable ⇒ Haagerup | ||
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| + | Property (T) and (F) ⇒ Residually finite | ||
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| + | Property (T) and Haagerup ⇔ finite | ||
| ===== Stability results ===== | ===== Stability results ===== | ||
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| ^[[residual_finiteness|Resid. finite]]| | | | | | | yes | | ^[[residual_finiteness|Resid. finite]]| | | | | | | yes | | ||
| ^[[kazhdan_property|Kazhdan (T)]] | | | | | | yes | | | ^[[kazhdan_property|Kazhdan (T)]] | | | | | | yes | | | ||
| - | ^[[haagerup_property|Haagerup]] | | yes | | | | | | | + | ^[[haagerup_property|Haagerup]] | | yes | | | yes | | | |
| - | ^[[amenability|Amenable]] | | no | | | yes | | | | + | ^[[amenability|Amenable]] | yes | no | | | yes | | | |
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| ^[[kazhdan_property|Kazhdan (T)]] | no | no | no | no | no | no | | no || | ^[[kazhdan_property|Kazhdan (T)]] | no | no | no | no | no | no | | no || | ||
| ^[[haagerup_property|Haagerup]] | yes | yes | yes | yes | yes | yes | | yes | yes | | | ^[[haagerup_property|Haagerup]] | yes | yes | yes | yes | yes | yes | | yes | yes | | | ||
| - | ^[[amenability|Amenable]] | | $N=2$ | | | | yes | | | | | | + | ^[[amenability|Amenable]] | no | $N=2$ | | | $N=4$ | yes | | no | $N=2$ | | |
| [(t:FO>Proven for $N\neq 3$)] | [(t:FO>Proven for $N\neq 3$)] | ||
approximation_properties_summary.1570198356.txt.gz · Last modified: 2021/11/23 11:56 (external edit)
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