{"paper":{"title":"Homology of SL2 over function fields I: parabolic subcomplexes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Matthias Wendt","submitted_at":"2014-04-23T13:54:26Z","abstract_excerpt":"The present paper studies the homology of the groups $SL_2(k[C])$ and $GL_2(k[C])$ where $C=\\overline{C}\\setminus\\{P_1,\\dots,P_s\\}$ is a smooth affine curve over an algebraically closed field $k$. It is well-known that these groups act on a product of trees and the quotients can be described in terms of certain equivalence classes of vector bundles on the complete curve. There is a natural subcomplex of cells with non-unipotent isotropy group. The paper provides explicit formulas for the equivariant homology of this \"parabolic subcomplex\". These formulas also describe the homology of $SL_2(k[C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5825","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"}