Rigidity in equivariant stable homotopy theory
Rigidity in equivariant stable homotopy theory
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DissertationPrüfungsdatum
29.07.2013Datum der Veröffentlichung
07.08.2013Erstgutachter
Schwede, StefanZweitgutachter
Greenlees, JohnMetadaten
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Inhalt
For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure'' of the 2-local G-equivariant stable homotopy category, such as the equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant version of Schwede's rigidity theorem at the prime 2.
Schlagwörter
Equivariant stable homotopy category, model category, rigidity
Klassifikation (DDC)
510 MathematikPatchkoria, Irakli: Rigidity in equivariant stable homotopy theory. - Bonn, 2013. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33024
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33024
@phdthesis{handle:20.500.11811/5732,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33024,
author = {{Irakli Patchkoria}},
title = {Rigidity in equivariant stable homotopy theory},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = aug,
note = {For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure'' of the 2-local G-equivariant stable homotopy category, such as the equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant version of Schwede's rigidity theorem at the prime 2.},
url = {https://hdl.handle.net/20.500.11811/5732}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-33024,
author = {{Irakli Patchkoria}},
title = {Rigidity in equivariant stable homotopy theory},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2013,
month = aug,
note = {For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor, homotopy cofiber sequences and the stable Burnside category determine all "higher order structure'' of the 2-local G-equivariant stable homotopy category, such as the equivariant homotopy types of function G-spaces. The theorem can be seen as an equivariant version of Schwede's rigidity theorem at the prime 2.},
url = {https://hdl.handle.net/20.500.11811/5732}
}
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