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Every connected component of $Teich_b$ is identified with its period space $P$ by global Torelli theorem. The mapping class group of $M$ acts on $P$ as a finite index subgroup of the group of isometries of the integer cohomology lattice, that is, satisfies assumptions of Ratner theorem. We prove that there are three classes of orbits"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.05802","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2017-08-19T03:53:07Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"015b6569f3dba43f13200cece0453b87c3fab6e8b40e40a43a7d12f58dbecbbc","abstract_canon_sha256":"6173978709ca3e64740a01fc59ef2f6a159bfe97493750370daf344314a8ba38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:44.219099Z","signature_b64":"2JU7D7ZQ1WwH2DJwwNwmW+TS4MmsU9bMHz5XOybcc7hh+LlwJRAA0A4jqsIJBFuTUilh7FEbrqpYg8nxtawpBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99194b021e500806a8c0215587a838d8a04f8927247e6612b5f0f6222cd807ed","last_reissued_at":"2026-05-18T00:37:44.218367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:44.218367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic complex structures on hyperkahler manifolds: an erratum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Misha Verbitsky","submitted_at":"2017-08-19T03:53:07Z","abstract_excerpt":"Let $M$ be a hyperkahler manifold, $\\Gamma$ its mapping class group, and $Teich$ the Teichmuller space of complex structures of hyperkahler type. 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