Heß, 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
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 = {http://hdl.handle.net/20.500.11811/5353}

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