Factorable MonoidsResolutions and Homology via Discrete Morse Theory
Factorable Monoids
Resolutions and Homology via Discrete Morse Theory
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DissertationDate of Exam
12.06.2012Date of Publication
26.07.2012Advisor
Bödigheimer, Carl-FriedrichCo-Referee
Lück, WolfgangMetadata
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Abstract
We study groups and monoids that are equipped with an extra structure called factorability.
A factorable group can be thought of as a group G together with the choice of a generating set S and a particularly well-behaved normal form map G → S*, where S* denotes the free group over S. This is related to the theory of complete rewriting systems, collapsing schemes and discrete Morse theory.
Given a factorable monoid M, we construct new resolutions of Z over the monoid ring ZM. These resolutions are often considerably smaller than the bar resolution E*M.
As an example, we show that a large class of generalized Thompson groups and monoids fits into the framework of factorability and compute their homology groups. In particular, we provide a purely combinatorial way of computing the homology of Thompson's group F.
A factorable group can be thought of as a group G together with the choice of a generating set S and a particularly well-behaved normal form map G → S*, where S* denotes the free group over S. This is related to the theory of complete rewriting systems, collapsing schemes and discrete Morse theory.
Given a factorable monoid M, we construct new resolutions of Z over the monoid ring ZM. These resolutions are often considerably smaller than the bar resolution E*M.
As an example, we show that a large class of generalized Thompson groups and monoids fits into the framework of factorability and compute their homology groups. In particular, we provide a purely combinatorial way of computing the homology of Thompson's group F.
Subjects
Gruppenhomologie, kombinatorische Gruppentheorie, diskrete Morsetheorie, Umschreibsystem, Neuschreibsystem, Termersetzungssystem, Thompsongruppe, Faktorabilität, faktorable Gruppe, faktorables Monoid, Kollabierschema, group homology, combinatorial group theory, discrete morse theory, rewriting system, thompson group, factorability, factorable group, factorable monoid, collapsing scheme
Classification (DDC)
510 MathematikHeß, Alexander: Factorable Monoids : Resolutions and Homology via Discrete Morse Theory. - Bonn, 2012. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29325
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29325
@phdthesis{handle:20.500.11811/5353,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29325,
author = {{Alexander Heß}},
title = {Factorable Monoids : Resolutions and Homology via Discrete Morse Theory},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = jul,
note = {We study groups and monoids that are equipped with an extra structure called factorability.
A factorable group can be thought of as a group G together with the choice of a generating set S and a particularly well-behaved normal form map G → S*, where S* denotes the free group over S. This is related to the theory of complete rewriting systems, collapsing schemes and discrete Morse theory.
Given a factorable monoid M, we construct new resolutions of Z over the monoid ring ZM. These resolutions are often considerably smaller than the bar resolution E*M.
As an example, we show that a large class of generalized Thompson groups and monoids fits into the framework of factorability and compute their homology groups. In particular, we provide a purely combinatorial way of computing the homology of Thompson's group F.},
url = {https://hdl.handle.net/20.500.11811/5353}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29325,
author = {{Alexander Heß}},
title = {Factorable Monoids : Resolutions and Homology via Discrete Morse Theory},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = jul,
note = {We study groups and monoids that are equipped with an extra structure called factorability.
A factorable group can be thought of as a group G together with the choice of a generating set S and a particularly well-behaved normal form map G → S*, where S* denotes the free group over S. This is related to the theory of complete rewriting systems, collapsing schemes and discrete Morse theory.
Given a factorable monoid M, we construct new resolutions of Z over the monoid ring ZM. These resolutions are often considerably smaller than the bar resolution E*M.
As an example, we show that a large class of generalized Thompson groups and monoids fits into the framework of factorability and compute their homology groups. In particular, we provide a purely combinatorial way of computing the homology of Thompson's group F.},
url = {https://hdl.handle.net/20.500.11811/5353}
}
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