{"paper":{"title":"Topological CoHochschild Homology and Thom Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Jiaxi Zha","submitted_at":"2026-01-16T13:11:43Z","abstract_excerpt":"For an $\\E$-ring spectrum $R$ and a map $f:X\\to Pic(R)$ of spaces, the Thom spectrum $\\T f$ is a comodule over $R\\otimes\\Si X$. In this paper we study the topological coHochschild homology of $R\\otimes\\Si X$ with coefficient $\\T f$. More concretely, for a simply connected space $X$, we will give a filtration on $\\mathrm{coTHH}^R(\\T f;R\\otimes\\Si X)$ via the cellular structure of $X$. Furthermore, we will reduce the computation of $\\mathrm{coTHH}^R(\\T f;R\\otimes\\Si X)$ to that of $\\mathrm{coTHH}^R(R\\otimes\\Si G)$ for some group-like $\\mathbb{E}_1$-spaces. Finally, we will use these results to s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.11263","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/2601.11263/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"}