{"paper":{"title":"Equivariant $K$-theory of GKM bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Catalin Zara, Silvia Sabatini, Victor Guillemin","submitted_at":"2012-03-05T19:54:28Z","abstract_excerpt":"Given a fiber bundle of GKM spaces, $\\pi\\colon M\\to B$, we analyze the structure of the equivariant $K$-ring of $M$ as a module over the equivariant $K$-ring of $B$ by translating the fiber bundle, $\\pi$, into a fiber bundle of GKM graphs and constructing, by combinatorial techniques, a basis of this module consisting of $K$-classes which are invariant under the natural holonomy action on the $K$-ring of $M$ of the fundamental group of the GKM graph of $B$. We also discuss the implications of this result for fiber bundles $\\pi\\colon M\\to B$ where $M$ and $B$ are generalized partial flag variet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1027","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":""},"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"}