On Operads
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2001051822
https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2001051822
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DC Element | Wert | Sprache |
---|---|---|
dc.contributor.advisor | Prof. Dr. Rainer Vogt | |
dc.creator | Brinkmeier, Michael | |
dc.date.accessioned | 2010-01-30T14:50:23Z | |
dc.date.available | 2010-01-30T14:50:23Z | |
dc.date.issued | 2001-05-18T14:28:06Z | |
dc.date.submitted | 2001-05-18T14:28:06Z | |
dc.identifier.uri | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2001051822 | - |
dc.description.abstract | This 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.iso | eng | |
dc.subject | Operads | |
dc.subject | Little Cubes | |
dc.subject | Tensorproduct of Operads | |
dc.subject | H-spaces | |
dc.subject | Strongly Homotopy Commutative | |
dc.subject | Homotopy Homomorphism | |
dc.subject | Permutohedron | |
dc.subject.ddc | 510 - Mathematik | |
dc.title | On Operads | eng |
dc.title.alternative | Über Operaden | ger |
dc.type | Dissertation oder Habilitation [doctoralThesis] | - |
thesis.location | Osnabrück | - |
thesis.institution | Universität | - |
thesis.type | Dissertation [thesis.doctoral] | - |
thesis.date | 2000-12-08T12:00:00Z | - |
elib.elibid | 91 | - |
elib.marc.edt | fangmeier | - |
elib.dct.accessRights | a | - |
elib.dct.created | 2000-12-13T15:16:45Z | - |
elib.dct.modified | 2001-05-18T14:28:06Z | - |
dc.contributor.referee | Dr. habil. Martin Markl | |
dc.subject.msc | 55P48 | eng |
dc.subject.msc | 55P35 | eng |
dc.subject.msc | 55P47 | eng |
dc.subject.msc | 55P45 | eng |
dc.subject.dnb | 27 - Mathematik | ger |
vCard.ORG | FB6 | ger |
Enthalten in den Sammlungen: | FB06 - E-Dissertationen |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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E-Diss91_thesis.tar.gz | 147,31 kB | GZIP | E-Diss91_thesis.tar.gz Öffnen/Anzeigen | |
E-Diss91_thesis.pdf | Präsentationsformat | 830,44 kB | Adobe PDF | E-Diss91_thesis.pdf Öffnen/Anzeigen |
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