{"paper":{"title":"The Getzler-Gauss-Manin connection and Kontsevich-Soibelman operations on the periodic cyclic homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.QA","authors_text":"Zihong Chen","submitted_at":"2026-01-23T04:26:23Z","abstract_excerpt":"We study equivariant operations on the periodic cyclic homology of dg algebras that arise from the chain level action of the two-colored Kontsevich-Soibelman operad. The first main result is that these operations are covariantly constant with respect to the Getzler-Gauss-Manin connection on the periodic cyclic homology of a family of dg algebras. Then, using classical computations of Cohen \\cite{Coh}, we explicitly compute a set of generators for these operations under composition, and show that these generators are closely related to the $p$-fold equivariant cap products previously studied by"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.16437","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2601.16437/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}