{"paper":{"title":"Yang-Mills theory over surfaces and the Atiyah-Segal theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.KT"],"primary_cat":"math.AT","authors_text":"Daniel A. Ramras","submitted_at":"2007-10-03T18:59:36Z","abstract_excerpt":"In this paper we explain how Morse theory for the Yang-Mills functional can be used to prove an analogue, for surface groups, of the Atiyah-Segal theorem. Classically, the Atiyah-Segal theorem relates the representation ring R(\\Gamma) of a compact Lie group $\\Gamma$ to the complex K-theory of the classifying space $B\\Gamma$. For infinite discrete groups, it is necessary to take into account deformations of representations, and with this in mind we replace the representation ring by Carlsson's deformation $K$--theory spectrum $\\K (\\Gamma)$ (the homotopy-theoretical analogue of $R(\\Gamma)$). Our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.0681","kind":"arxiv","version":5},"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"}