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If the fixed-point set $X^T$ has the homotopy type of a finite W-CW complex, we prove that the rationalized complex equivariant K-theory of X is a free module over the representation ring of G. Given additional conditions on the W-action on the fixed-point set $X^T$ we show that the equivariant K-theory of X is free over R(G). We use this to provide computat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.4748","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-03-21T14:42:59Z","cross_cats_sorted":[],"title_canon_sha256":"88217dee02997dbfddcf67fc42b0d44526a6c9e1f4d897b833f4ef85b224a6ab","abstract_canon_sha256":"841bda1553e62e5a6ee5d1b0f9c2764077abf646ac8ce8cfc89aaa04437bd89c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.680249Z","signature_b64":"JQqZPlPAV3Teo9/ZdhZBGwp5Reha0GfiwqzYRfz7hw0I53qVoaqMuSRfX1o6r36zyI8W0mjRMPlymLuHY/XsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a550b222fc08cd68e2f21894fa26f12d949401be6840952f703c93a516afd77","last_reissued_at":"2026-05-18T02:57:53.679664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.679664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Equivariant K-theory of compact Lie group actions with maximal rank isotropy","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":"2012-03-21T14:42:59Z","abstract_excerpt":"Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected subgroups of maximal rank. Let $T\\subset G$ be a maximal torus with Weyl group W. If the fixed-point set $X^T$ has the homotopy type of a finite W-CW complex, we prove that the rationalized complex equivariant K-theory of X is a free module over the representation ring of G. Given additional conditions on the W-action on the fixed-point set $X^T$ we show that the equivariant K-theory of X is free over R(G). 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