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
Titel: | On Operads |
Sonstige Titel: | Über Operaden |
Autor(en): | Brinkmeier, Michael |
Erstgutachter: | Prof. Dr. Rainer Vogt |
Zweitgutachter: | Dr. habil. Martin Markl |
Zusammenfassung: | 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. |
URL: | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2001051822 |
Schlagworte: | Operads; Little Cubes; Tensorproduct of Operads; H-spaces; Strongly Homotopy Commutative; Homotopy Homomorphism; Permutohedron |
Erscheinungsdatum: | 18-Mai-2001 |
Einreichungsdatum: | 18-Mai-2001 |
Publikationstyp: | Dissertation oder Habilitation [doctoralThesis] |
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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