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Fibrations and Idempotent Functors
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two articles. Both articles concern homotopical algebra. In Paper I we study functors indexed by a small category into a model category whose value at each morphism is a weak equivalence. We show that the category of such functors can be understood as a certain mapping space. Specializing to topological spaces, this result is used to reprove a classical theorem that classifies fibrations with a fixed base and homotopy fiber. In Paper II we study augmented idempotent functors, i.e., co-localizations, operating on the category of groups. We relate these functors to cellular coverings of groups and show that a number of properties, such as finiteness, nilpotency etc., are preserved by such functors. Furthermore, we classify the values that such functors can take upon finite simple groups and give an explicit construction of such values.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. , vii, 26 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 11:11
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-66740ISBN: 978-91-7502-235-3 OAI: oai:DiVA.org:kth-66740DiVA: diva2:484557
Public defence
2012-01-31, Sal F3, Lindstedtsvägen 26, KTH, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20120127Available from: 2012-01-27 Created: 2012-01-27 Last updated: 2012-02-10Bibliographically approved
List of papers
1. On the classification of fibrations
Open this publication in new window or tab >>On the classification of fibrations
2015 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 367, no 1, 519-557 p.Article in journal (Refereed) Published
Abstract [en]

We identify the homotopy type of the moduli of maps with a given homotopy type of the base and the homotopy fiber. A new model for the space of weak equivalences and its classifying space is given.

National Category
Algebra and Logic
Identifiers
urn:nbn:se:kth:diva-66736 (URN)10.1090/S0002-9947-2014-06142-4 (DOI)000344826400019 ()2-s2.0-84924794787 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation, KAW2005.0098Swedish Research Council
Note

QC 20150115. Updated from manuscript to article in journal.

Available from: 2012-01-27 Created: 2012-01-27 Last updated: 2017-12-08Bibliographically approved
2. Idempotent deformations of finite groups
Open this publication in new window or tab >>Idempotent deformations of finite groups
(English)Manuscript (preprint) (Other academic)
National Category
Algebra and Logic
Identifiers
urn:nbn:se:kth:diva-66737 (URN)
Note
QS 2012Available from: 2012-01-27 Created: 2012-01-27 Last updated: 2012-01-27Bibliographically approved

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