A category of pseudo-tangles with classifying space Ω∞ S∞ and applications
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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2000090826
Title: | A category of pseudo-tangles with classifying space Ω∞ S∞ and applications |
Other Titles: | Eine Kategorie aus Pseudo-Verschlingungen mit klassifizierendem Raum Ω∞ S∞ und Anwendungen |
Authors: | Blömer, Olaf |
Thesis advisor: | Prof. Dr. Rainer Vogt |
Thesis referee: | Prof. Dr. Christian Kassel |
Abstract: | It is well known that the group completion of the classifying space of the free permutative category is Ω∞ S∞, i.e. stable homotopy of the 0-sphere. Quillen´s S-1S construction can be applied to the free permutative category, which has a pictorial description by pseudo-tangles, and this leads to another pictorial descripted category G which has the classifying space Ω∞ S∞. With help of this model G we can give generators for the homotopy groups of Ω∞ S∞ for i=0,1,2. As a further application, we compute the fundamental group of the free permutative category with duality and show that the association of a duality structure on the categorial level does not lead to a group completion on the level of classifying spaces. |
URL: | https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2000090826 |
Subject Keywords: | stable homotopy of spheres; classifying space; free permutative category; duality; group completion; tangles |
Issue Date: | 8-Sep-2000 |
Submission date: | 8-Sep-2000 |
Type of publication: | Dissertation oder Habilitation [doctoralThesis] |
Appears in Collections: | FB06 - E-Dissertationen |
Files in This Item:
File | Description | Size | Format | |
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E-Diss8_bloemer.tar.gz | 838,35 kB | GZIP | E-Diss8_bloemer.tar.gz View/Open | |
E-Diss8_volldiss.ps.gz | 279,44 kB | GZIP | E-Diss8_volldiss.ps.gz View/Open |
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