{"paper":{"title":"Smooth atlas stratified spaces, K-Homology Orientations, and Gysin maps. Part 2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.KT"],"primary_cat":"math.AT","authors_text":"Markus Banagl, Paolo Piazza, Pierre Albin","submitted_at":"2026-05-27T15:29:29Z","abstract_excerpt":"In this Part 2 of our article we give a detailed discussion of the compatibility between the analytic Gysin maps we have defined in Part 1 and the topological Gysin maps defined by the second author. A significant role is played by a bordism-like description of K-homology due to Jakob which is closely related to the geometric K-homology theory of Baum and Douglas. We give a self-contained proof of the equivalence of the former with the analytic K-homology theory of Kasparov. As an intermediate step towards proving our main result we use Thom's transversality theorem to describe Gysin maps comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28620","kind":"arxiv","version":1},"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/2605.28620/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"}