The homotopy groups of a homotopy group completion

dc.contributor.authorRamras, Daniel A.
dc.contributor.departmentMathematical Sciences, School of Scienceen_US
dc.date.accessioned2020-06-19T20:28:45Z
dc.date.available2020-06-19T20:28:45Z
dc.date.issued2019
dc.description.abstractLet M be a topological monoid with homotopy group completion ΩBM. Under a strong homotopy commutativity hypothesis on M, we show that πk(ΩBM) is the quotient of the monoid of free homotopy classes [Sk, M] by its submonoid of nullhomotopic maps. We give two applications. First, this result gives a concrete description of the Lawson homology of a complex projective variety in terms of pointwise addition of spherical families of effective algebraic cycles. Second, we apply this result to monoids built from the unitary, or general linear, representation spaces of discrete groups, leading to results about lifting continuous families of characters to continuous families of representations.en_US
dc.eprint.versionAuthor's manuscripten_US
dc.identifier.citationRamras, D. A. (2019). The homotopy groups of a homotopy group completion. Israel Journal of Mathematics, 234(1), 81–124. https://doi.org/10.1007/s11856-019-1914-2en_US
dc.identifier.urihttps://hdl.handle.net/1805/23021
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.isversionof10.1007/s11856-019-1914-2en_US
dc.relation.journalIsrael Journal of Mathematicsen_US
dc.rightsPublisher Policyen_US
dc.sourceArXiven_US
dc.subjecthomotopy group completionen_US
dc.subjectLawson homologyen_US
dc.subjectfamilies of charactersen_US
dc.titleThe homotopy groups of a homotopy group completionen_US
dc.typeArticleen_US
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