On Operads

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dc.contributor.advisorProf. Dr. Rainer Vogt
dc.creatorBrinkmeier, Michael
dc.date.accessioned2010-01-30T14:50:23Z
dc.date.available2010-01-30T14:50:23Z
dc.date.issued2001-05-18T14:28:06Z
dc.date.submitted2001-05-18T14:28:06Z
dc.identifier.urihttps://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2001051822-
dc.description.abstractThis Thesis consists of four independent parts. In the first part I prove that the delooping, i.e.the classifying space, of a grouplike monoid is an $H$-space if and only if its multiplication is a homotopy homomorphism. This is an extension and clarification of a result of Sugawara. Furthermore I prove that the Moore loop space functor and the construction of the classifying space induce an adjunction on the corresponding homotopy categories. In the second part I extend a result of G. Dunn, by proving that the tensorproduct $C_{n_1}\otimes\dots \otimes C_{n_j}$ of little cube operads is a topologically equivalent suboperad of $C_{n_1 \dots n_j}$. In the third part I describe operads as algebras over a certain colored operad. By application of results of Boardman and Vogt I describe a model of the homotopy category of topological operads and algebras over them, as well as a notion of lax operads, i.e. operads whose axioms are weakened up to coherent homotopies. Here the W-construction, a functorial cofibrant replacement for a topological operad, plays a central role. As one application I construct a model for the homotopy category of topological categories. C. Berger claimed to have constructed an operad structure on the permutohedras, whose associated monad is exactly the Milgram-construction of the free two-fold loop space. In the fourth part I prove that this statement is not correct.eng
dc.language.isoeng
dc.subjectOperads
dc.subjectLittle Cubes
dc.subjectTensorproduct of Operads
dc.subjectH-spaces
dc.subjectStrongly Homotopy Commutative
dc.subjectHomotopy Homomorphism
dc.subjectPermutohedron
dc.subject.ddc510 - Mathematik
dc.titleOn Operadseng
dc.title.alternativeÜber Operadenger
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2000-12-08T12:00:00Z-
elib.elibid91-
elib.marc.edtfangmeier-
elib.dct.accessRightsa-
elib.dct.created2000-12-13T15:16:45Z-
elib.dct.modified2001-05-18T14:28:06Z-
dc.contributor.refereeDr. habil. Martin Markl
dc.subject.msc55P48eng
dc.subject.msc55P35eng
dc.subject.msc55P47eng
dc.subject.msc55P45eng
dc.subject.dnb27 - Mathematikger
vCard.ORGFB6ger
Appears in Collections:FB06 - E-Dissertationen

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