A category of pseudo-tangles with classifying space Ω∞ S∞ and applications

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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://repositorium.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
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB06 - E-Dissertationen

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