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OP-8526Status unassessedGeometry and topology

Orbit Equivalence of Measure Preserving Actions · Question 2.1

L2L^2 invariants and their relatives for finitely generated groups · Historical workshop question

Editorial mapping of AIMPL source category: Geometric group theory. http://aimpl.org/l2invariantsgroups/ Not an author-supplied MSC code.

Historical list · status unassessedAs of 2026-09-08Source & evidence ↓

Problem statement

Let Γ1\Gamma_1 and Γ2\Gamma_2 be infinite countable groups. Does Γ1×Γ2\Gamma_1\times\Gamma_2 have fixed price 11?

Lean 4

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Background

Workshop introduction

This problem list concerns the study of the asymptotic behavior of some natural invariants of finitely generated groups.

Progress & source assessment

Historical workshop record. Current open/solved status has not been independently reassessed.

Status note in the source

By Abert-Weiss, it is enough to show that Bernoulli action of Γ1×Γ2\Gamma_1\times\Gamma_2 have cost equals to 11.

References
  1. [1]$L^2$ invariants and their relatives for finitely generated groups link

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