Compact domination for groups definable in linear o-minimal structures

Eleftheriou, Pantelis E.

doi:10.1007/s00153-009-0139-1

Cited by 7 publications

(3 citation statements)

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“…Remark 4.13. It is worth mentioning that in [18], following the proof of Pillay's Conjecture, the Compact Domination Conjecture was introduced, and was proved by splitting different cases in [11,15,19,20]. Compact Domination for an NIP group G turned out to be a crucial property, as it corresponds to the existence of an invariant smooth Keisler measure on G [30,Theorem 8.37].…”

Section: Claim 2 ν Is Left-invariantmentioning

confidence: 99%

Pillay's conjecture for groups definable in weakly o‐minimal non‐valuational structures

Eleftheriou

2021

Bull. London Math. Soc.

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Section: Claim 2 ν Is Left-invariantmentioning

confidence: 99%

Pillay's conjecture for groups definable in weakly o‐minimal non‐valuational structures

Eleftheriou

2021

Bull. London Math. Soc.

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“…Remark 4.12. It is worth mentioning that in [18], following the proof of Pillay's Conjecture, the Compact Domination Conjecture was introduced, and was proved by splitting different cases in [11,15,19,20]. Compact Domination for a NIP group G turned out to be a crucial property, as it corresponds to the existence of an invariant smooth Keisler measure on G ([30, Theorem 8.37]).…”

Section: Letmentioning

confidence: 99%

Groups definable in weakly o-minimal non-valuational structures

Eleftheriou

2020

Preprint

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Let M be a weakly o-minimal non-valuational structure, and N its canonical o-minimal extension (by Wencel). We prove that every group G definable in M is a subgroup of a group K definable in N , which is canonical in the sense that it is the smallest such group. As an application, we obtain that G 00 = G ∩ K 00 , and establish Pillay's Conjecture in this setting: G/G 00 , equipped with the logic topology, is a compact Lie group, and if G has finitely satisfiable generics, then dim Lie (G/G 00 ) = dim(G).

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“…On the other hand, the compact domination conjecture formalizes the idea that the quotient map in Pillay's conjecture should be a kind of intrinsic "standard part map". These conjectures lead to the development of new model theoretic tools as well as new geometric tools in o-minimality ( [7], [8], [9], [10], [12], [13], [14], [15], [16]). Corollary 1.3 Suppose that N is an o-minimal expansion of an ordered group.…”

Section: Introductionmentioning

confidence: 99%