{"paper":{"title":"Spectral gap property and strong ergodicity for groups of affine transformations of solenoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bachir Bekka, Camille Francini","submitted_at":"2018-02-25T12:56:45Z","abstract_excerpt":"Let X be a solenoid, that is, a compact finite dimensional connected abelian group with normalized Haar measure m, and let G be a countable discrete group acting on X by continuous affine transformations. We show that the probability measure preserving action of G on (X,m) does not have the spectral gap property if and only if there exists a p(G)-invariant proper subsolenoid Y of X such that the image of G in the affine group Aff(X/Y) of X/Y is a virtually solvable group, where p(G) is the automorphism part of G. When G is finitely generated or when X is a p-adic solenoid, the subsolenoid Y ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08996","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}