Factorable Groups and their Homology
Factorable Groups and their Homology
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DissertationDate of Exam
15.04.2011Date of Publication
04.07.2011Advisor
Bödigheimer, Carl-FriedrichCo-Referee
Stroppel, CatharinaMetadata
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Abstract
In this thesis we introduce the class of factorable groups. These are normed groups together with a norm preserving decemposition (or factorization) of each group element into two factors.
Already the norm alone gives a filtration of the bar resolution and of the bar complex, which we call the norm filtration and we study the spectral sequence associated to the norm filtration.
The main result of the thesis is that for a factorable group the homology of the columns of the E^0-term is concentrated in the top degree. Consequently, the spectral sequence associated to the norm filtration collapses after the E^2-term and the homology of the group G can be computed as the homology of the E^1-term.
Moreover, using the structure of a factorable group G we can find a free resolution of Z over ZG which has fewer generators than the bar resolution, making computations easier.
Already the norm alone gives a filtration of the bar resolution and of the bar complex, which we call the norm filtration and we study the spectral sequence associated to the norm filtration.
The main result of the thesis is that for a factorable group the homology of the columns of the E^0-term is concentrated in the top degree. Consequently, the spectral sequence associated to the norm filtration collapses after the E^2-term and the homology of the group G can be computed as the homology of the E^1-term.
Moreover, using the structure of a factorable group G we can find a free resolution of Z over ZG which has fewer generators than the bar resolution, making computations easier.
Subjects
algebraic topology, cohomology of groups
Classification (DDC)
510 MathematikVisy, Balázs: Factorable Groups and their Homology. - Bonn, 2011. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25590
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25590
@phdthesis{handle:20.500.11811/4990,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25590,
author = {{Balázs Visy}},
title = {Factorable Groups and their Homology},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2011,
month = jul,
note = {In this thesis we introduce the class of factorable groups. These are normed groups together with a norm preserving decemposition (or factorization) of each group element into two factors.
Already the norm alone gives a filtration of the bar resolution and of the bar complex, which we call the norm filtration and we study the spectral sequence associated to the norm filtration.
The main result of the thesis is that for a factorable group the homology of the columns of the E^0-term is concentrated in the top degree. Consequently, the spectral sequence associated to the norm filtration collapses after the E^2-term and the homology of the group G can be computed as the homology of the E^1-term.
Moreover, using the structure of a factorable group G we can find a free resolution of Z over ZG which has fewer generators than the bar resolution, making computations easier.},
url = {https://hdl.handle.net/20.500.11811/4990}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-25590,
author = {{Balázs Visy}},
title = {Factorable Groups and their Homology},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2011,
month = jul,
note = {In this thesis we introduce the class of factorable groups. These are normed groups together with a norm preserving decemposition (or factorization) of each group element into two factors.
Already the norm alone gives a filtration of the bar resolution and of the bar complex, which we call the norm filtration and we study the spectral sequence associated to the norm filtration.
The main result of the thesis is that for a factorable group the homology of the columns of the E^0-term is concentrated in the top degree. Consequently, the spectral sequence associated to the norm filtration collapses after the E^2-term and the homology of the group G can be computed as the homology of the E^1-term.
Moreover, using the structure of a factorable group G we can find a free resolution of Z over ZG which has fewer generators than the bar resolution, making computations easier.},
url = {https://hdl.handle.net/20.500.11811/4990}
}
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