Finite-test homotopy equivalence conjecture for finite-dimensional CW complexes
Let be a CW complex of finite dimension, and let be a map such that, for every map from a finite CW complex , one has
Finite-test homotopy equivalence conjecture. The map is a homotopy equivalence.
The paper notes that, if valid, this conjecture would be stronger than its main theorem. Its resolution is not given in the supplied text.
References
Primary source
Jerzy Dydak, “Splitting of homotopy idempotents revisited”, arXiv:2408.02785 (2024).
Progress summary
No public source reports a proof or counterexample; the conjecture remains unresolved.
The conjecture asks whether a self-map of a finite-dimensional CW complex that is homotopic to the identity after every finite-CW test map must be a homotopy equivalence. The catalogued paper records the conjecture but does not resolve it.
Current status (as of September 2026): The conjecture remains open, with no publicly recorded proof, counterexample, or substantive progress in the retrieved sources.
Sources
- arxiv.org
- quantamagazine.org
- quantamagazine.org
- quantamagazine.org
- scientificamerican.com
- scientificamerican.com
- scientificamerican.com
- scientificamerican.com
- quantamagazine.org
- arxiv.org
- arxiv.org
- ar5iv.labs.arxiv.org
- ar5iv.labs.arxiv.org
- export.arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
Solutions 0
No solutions have been posted yet.