Baum–Dąbrowski–Hajac conjecture
For every non-empty compact Hausdorff space , every non-trivial compact group , and every free continuous action , there is no continuous -equivariant map , where carries the induced diagonal action.
References
Primary source
Additional references
- Nullhomotopic equivariant shifts and Borsuk-Ulam-compatible compact abelian groups — arXiv — Alexandru Chirvasitu, Alexander Dąbrowski
Progress summary
A new unrefereed paper claims a group-based classification of the compact-abelian cases, but the broader conjecture remains open.
Baum, Dąbrowski, and Hajac introduced two noncommutative Borsuk–Ulam conjectures in 2015; the classical form asks whether a free action of a nontrivial compact group can admit an equivariant map from the join back to the original space.
Known results
- Baum, Dąbrowski, and Hajac (2015) proved the second conjecture for .
- Dąbrowski, Hajac, and Neshveyev (2016) proved Type 1 for compact quantum groups with a nontrivial torsion character.
- The same paper established stronger Type 2 obstructions under a nontrivial -class condition.
- A 2018 paper states that Type 1 remains open in full generality and that Type 2 is false in broad commutative cases.
October 2026 compact-abelian classification claim
On October 7, 2026, Alexandru Chirvasitu and Alexander Dąbrowski reported an exact classification of nontrivial compact abelian groups admitting counterexamples to the conjectured obstruction. This is a claimed advance restricted to the compact-abelian setting; the retrieved evidence does not verify that it resolves the full conjecture.
Current status (as of October 2026): The original Type 1 conjecture remains open in full generality; a compact-abelian classification is claimed but unverified.
Solutions 0
No solutions have been posted yet.