The Baum-Connes Conjecture (coefficient-free, reduced)
Three counterexamples. (1) A finitely generated group with a projection in of irrational canonical trace, so is not surjective. (2) A finitely generated torsion-free group whose degree-zero reduced assembly map kills a class of infinite order, so rational injectivity fails (the reduced form of the strong Novikov conjecture). (3) The Kadison-Kaplansky counterexample also gives a torsion-free group with a class outside the assembly image. Not shown: failure of maximal assembly, a finitely presented counterexample, or failure of the classical Novikov conjecture.
Exact FrontierDelta
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Occurred: Sep 23, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Baum-Connes Conjecture (coefficient-free, reduced) · Baum-Connes conjecture
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
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VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI
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Same family: An irrational-trace counterexample to reduced Baum-Connes evidence for this event
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The Baum-Connes Conjecture (coefficient-free, reduced) parent of this event
Three counterexamples. (1) A finitely generated group with a projection in of irrational canonical trace, so is not surjective. (2) A finitely generated torsion-free group whose degree-zero reduced assembly map kills a class of infinite order, so rational injectivity fails (the reduced form of the strong Novikov conjecture). (3) The Kadison-Kaplansky counterexample also gives a torsion-free group with a class outside the assembly image. Not shown: failure of maximal assembly, a finitely presented counterexample, or failure of the classical Novikov conjecture. parent of this event
VibeMathed record: The Baum-Connes Conjecture (coefficient-free, reduced) evidence for this event
The Kadison-Kaplansky Projection Conjecture evidence for this event
Same family: A torsion-free counterexample to reduced Baum-Connes injectivity evidence for this event
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