Measurable Imbeddings, Free Products, and Graph Products
\"Ozkan Demir

TL;DR
This paper investigates a generalized form of measure-based group embedding called Measurable Imbeddability, demonstrating how such embeddings behave under free and graph product constructions.
Contribution
It establishes that Measurable Imbeddability is preserved under free and graph product operations given certain conditions, extending previous understanding of measure-theoretic group relations.
Findings
Measurable Imbeddability is preserved under free products with specific assumptions.
The result extends to graph products of groups.
Provides new techniques for analyzing measure-theoretic group embeddings.
Abstract
We study Measurable Imbeddability between groups, which is an order-like generalization of Measure Equivalence that allows the imbedded group to have an infinite measure fundamental domain. We prove if measurably imbeds into , and measurably imbeds into under an additional assumption that lets the corresponding fundamental domains to be arranged in a special way, then measurably imbeds into . Building upon the techniques we used, we show that the analogous result holds for graph products of groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Holomorphic and Operator Theory
