Connor MacMahon

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math.GR2026

Existential Inclusions of Bi-exact Groups are Conjugacy Representation Rigid

Connor MacMahon

If $Λ$ is a non-amenable bi-exact group and $Λ ↪ Γ$ is an existential embedding, then each of the intersections $Λ \cap g Λ g^{- 1}$ for $g$ a member of $Γ\Λ$ i…

math.GR2026

An $ℓ^{2}$ Obstruction for Elementary Embeddings of Hyperbolic Groups

Connor MacMahon

The first $ℓ^{2}$ Betti number of a group is non-decreasing under various embeddings arising from first order logic. Strict inequality is proved for elementary embeddings of non-a…

Existential Inclusions of Bi-exact Groups are Conjugacy Representation Rigid

An ℓ2 Obstruction for Elementary Embeddings of Hyperbolic Groups

An $ℓ^{2}$ Obstruction for Elementary Embeddings of Hyperbolic Groups