The Hotel of Algebraic Surgery
The Hotel of Algebraic Surgery
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DissertationPrüfungsdatum
26.06.2014Datum der Veröffentlichung
09.07.2014Erstgutachter
Lück, WolfgangZweitgutachter
Ranicki, Andrew A.Metadaten
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Inhalt
We revisit the algebraic surgery theory and especially the proof of the total surgery obstruction.
The total surgery obstruction was defined by Ranicki for a finite n-dimensional Poincaré complex X as an element in a certain abelian group with the property that for n≥5 it vanishes if and only if X is homotopy equivalent to a closed n-dimensional manifold.
This thesis adds details that were missing in the original sources and provides a self-contained proof.
In order to make the proof and the underlying algebraic surgery theory more easily accessible, the proof is presented in various levels with each level supplying more elaborate details.
The total surgery obstruction was defined by Ranicki for a finite n-dimensional Poincaré complex X as an element in a certain abelian group with the property that for n≥5 it vanishes if and only if X is homotopy equivalent to a closed n-dimensional manifold.
This thesis adds details that were missing in the original sources and provides a self-contained proof.
In order to make the proof and the underlying algebraic surgery theory more easily accessible, the proof is presented in various levels with each level supplying more elaborate details.
Schlagwörter
L-Theorie, L-Gruppen, Klassifikation von Mannigfaltigkeiten, algebraische Chirurgie, Chirurgiehindernis, L-Theory, L-groups, classification of manifolds, algebraic surgery theory, total surgery obstruction, Surgery obstructions, Wall groups
Klassifikation (DDC)
510 MathematikKühl, Philipp: The Hotel of Algebraic Surgery. - Bonn, 2014. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36778
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36778
@phdthesis{handle:20.500.11811/6127,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36778,
author = {{Philipp Kühl}},
title = {The Hotel of Algebraic Surgery},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = jul,
note = {We revisit the algebraic surgery theory and especially the proof of the total surgery obstruction.
The total surgery obstruction was defined by Ranicki for a finite n-dimensional Poincaré complex X as an element in a certain abelian group with the property that for n≥5 it vanishes if and only if X is homotopy equivalent to a closed n-dimensional manifold.
This thesis adds details that were missing in the original sources and provides a self-contained proof.
In order to make the proof and the underlying algebraic surgery theory more easily accessible, the proof is presented in various levels with each level supplying more elaborate details.},
url = {https://hdl.handle.net/20.500.11811/6127}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36778,
author = {{Philipp Kühl}},
title = {The Hotel of Algebraic Surgery},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = jul,
note = {We revisit the algebraic surgery theory and especially the proof of the total surgery obstruction.
The total surgery obstruction was defined by Ranicki for a finite n-dimensional Poincaré complex X as an element in a certain abelian group with the property that for n≥5 it vanishes if and only if X is homotopy equivalent to a closed n-dimensional manifold.
This thesis adds details that were missing in the original sources and provides a self-contained proof.
In order to make the proof and the underlying algebraic surgery theory more easily accessible, the proof is presented in various levels with each level supplying more elaborate details.},
url = {https://hdl.handle.net/20.500.11811/6127}
}
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