A finite loop space not rationally equivalent to a compact Lie group

• 成果类型: Article
• 署名作者: Andersen, KKS; Bauer, T; Grodal, J; Pedersen, EK
• 署名单位: Aarhus University; University of Munster; University of Chicago; State University of New York (SUNY) System; Binghamton University, SUNY
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-003-0341-4
• 发表日期: 2004
• 页码: 1-10
• 关键词: associative h-spaces; principal s3-bundles; polynomial algebras; realization; COHOMOLOGY; PRODUCTS; spheres

摘要

We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5.