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Beschreibung:
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 Z M. 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.