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

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dc.creatorAndersen, Kasper K. S.
dc.creatorBauer, Tilman
dc.creatorGrodal, Jesper
dc.creatorPedersen, Erik K.
dc.date2003-06-16
dc.date.accessioned2026-07-07T04:58:59Z
dc.date.available2026-07-07T04:58:59Z
dc.descriptionWe 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.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/math/0306234
dc.identifierhttp://arxiv.org/abs/math/0306234
dc.identifierInvent. Math 157 (2004), no. 1, 1--10.
dc.identifierdoi:10.1007/s00222-003-0341-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67800
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject55P35; 55P15, 55R35
dc.titleA finite loop space not rationally equivalent to a compact Lie group
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