{"paper":{"title":"A classifying space for commutativity in Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Alejandro Adem, Jos\\'e Manuel G\\'omez","submitted_at":"2013-08-31T15:50:58Z","abstract_excerpt":"In this article we consider a space B_{com}G assembled from commuting elements in a Lie group G first defined in [Adem, Cohen, Torres-Giese 2012]. We describe homotopy-theoretic properties of these spaces using homotopy colimits, and their role as a classifying space for transitionally commutative bundles. We prove that ZxB_{com}U is a loop space and define a notion of commutative K-theory for bundles over a finite complex X which is isomorphic to [X,ZxB_{com}U]. We compute the rational cohomology of B_{com}G for G equal to any of the classical groups U(n), SU(n) and Sp(n), and exhibit the rat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0128","kind":"arxiv","version":3},"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"}