{"paper":{"title":"Landweber exact formal group laws and smooth cohomology theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GT"],"primary_cat":"math.KT","authors_text":"Ingo Schroeder (Georg-August-Universit\\\"at G\\\"ottingen), Moritz Wiethaup (Georg-August-Universit\\\"at G\\\"ottingen), Thomas Schick (Georg-August-Universit\\\"at G\\\"ottingen), Ulrich Bunke (Regensburg)","submitted_at":"2007-11-07T18:24:37Z","abstract_excerpt":"The main aim of this paper is the construction of a smooth (sometimes called differential) extension \\hat{MU} of the cohomology theory complex cobordism MU, using cycles for \\hat{MU}(M) which are essentially proper maps W\\to M with a fixed U(n)-structure and U(n)-connection on the (stable) normal bundle of W\\to M. Crucial is that this model allows the construction of a product structure and of pushdown maps for this smooth extension of MU, which have all the expected properties. Moreover, we show, using the Landweber exact functor principle, that \\hat{R}(M):=\\hat{MU}(M)\\otimes_{MU^*}R defines "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.1134","kind":"arxiv","version":6},"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"}