Torsion and the torsion-free quotient of homology cobordism
A question from Bulletin of the American Mathematical Society (2024). Problem O; inspected PDF p. 13.
Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.
Problem statement
Does the smooth integral homology cobordism group contain an element of finite order greater than one? Is its quotient by the torsion subgroup free abelian?
Lean 4
No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.
Background
Editorial summary of Problem O; inspected PDF p. 13 in A survey of the homology cobordism group. Read the original for the full definitions and context.
Bulletin AMS 61 (2024), 119–157. Locators refer to the 32-page arXiv v4 author manuscript, not journal pagination.
Progress & source assessment
The source presents this question or research direction as unresolved at the time of writing. Current status has not been independently established. Source inspected on 2026-09-10; this date is a provenance check, not certification that the question remains open.
- [1]Oğuz Şavk. A survey of the homology cobordism group. Bulletin of the American Mathematical Society (2024). linkProblem O; inspected PDF p. 13
Recorded progress
Add yours →Nothing recorded yet. A pointer to a paper the entry is missing counts.
Machine attempts
0 recordedAttempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.
No machine attempts recorded.
Sign in to run an attempt. New accounts start with enough credits for ten.
Discussion
0 notesNotes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.
No notes yet.
Sign in to add a note.