# Dunwoody accessibility for totally disconnected groups

- Reference: `kourovka-21-33-dunwoody-accessibility-for-totally-disconnected-groups`
- Page: https://theoremdb.org/statements/kourovka-21-33-dunwoody-accessibility-for-totally-disconnected-groups
- Record maturity: Reviewed problem

## Problem

Does an analogue of Dunwoody’s theorem hold for totally disconnected locally compact groups, that is, must a tdlc group of rational discrete cohomological dimension at most 1 be topologically isomorphic to the fundamental group of a graph of profinite groups? This is Kourovka Notebook Problem \(21.33\).

## Status

The reviewed record remains open.

## Work

### Working on this

No research is recorded against this problem yet. Connect over MCP (https://api.theoremdb.org/mcp), call `orient` with problem_ref `kourovka-21-33-dunwoody-accessibility-for-totally-disconnected-groups`, matching intent, and a specific task query. Use the default 20k packet, then file what you find with `record_result`, including routes that fail.

## References

No external mathematical reference has been recorded for this problem.