The Bestvina-Brady Construction Revisited: Geometric Computation of {sum}-Invariants for Right-Angled Artin Groups |
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Authors: | Bux Kai-Uwe; Gonzalez Carlos |
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Institution: | Department of Mathematics Room 233, 155 S, 1400 E, University of Utah Salt Lake City, UT 84122-0090, USA, kubux{at}gmx.net
Fachbereich Mathematik, Johann Wolfgang Goethe-Universität D-60054 Frankfurt-am-Main, Germany, gonzalez{at}secude.com |
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Abstract: | The starting point of our investigation is the remarkable paper2] in which Bestvina and Brady gave an example of an infinitelyrelated group of type FP2. The result about right-angled Artingroups behind their example is best interpreted by means ofthe BieriStrebelNeumannRenz -invariants. For a group G the invariants n(G) and n(G, Z) are sets of non-trivialhomomorphisms :GR. They contain full information about finitenessproperties of subgroups of G with abelian factor groups. Themain result of 2] determines for the canonical homomorphism, taking each generator of the right-angled Artin group G to1, the maximal n with n(G), respectively n(G, Z). In 6] Meier, Meinert and VanWyk completed the picture by computingthe full -invariants of right-angled Artin groups using as wellthe result of Bestvina and Brady as algebraic techniques from-theory. Here we offer a new account of their result which istotally geometric. In fact, we return to the BestvinaBradyconstruction and simplify their argument considerably by bringinga more general notion of links into play. At the end of thefirst section we re-prove their main result. By re-computingthe full -invariants, we show in the second section that thesimplification even adds some power to the method. The criterionwe give provides new insight on the geometric nature of then-domination condition employed in 6]. |
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