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Search Results: 1 - 10 of 20483 matches for " Kim Ruane "
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CAT(0) groups with specified boundary
Kim Ruane
Mathematics , 2009, DOI: 10.2140/agt.2006.6.633
Abstract: We specify exactly which groups can act geometrically on CAT(0) spaces whose visual boundary is homeomorphic to either a circle or a suspension of a Cantor set.
Some geometric groups with rapid decay
Indira Chatterji,Kim Ruane
Mathematics , 2003,
Abstract: We explain some simple methods to establish the property of Rapid Decay for a number of groups arising geometrically. We also give new examples of groups with the property of Rapid Decay. In particular we establish the property of Rapid Decay for all lattices in rank one Lie groups.
CAT(0) cubical complexes for graph products of finitely generated abelian groups
Kim Ruane,Stefan Witzel
Mathematics , 2013,
Abstract: We show that every graph product of finitely generated abelian groups acts properly and cocompactly on a CAT(0) cubical complex. The complex generalizes (up to subdivision) the Salvetti complex of a right-angled Artin group and the Coxeter complex of a right-angled Coxeter group. In the right-angled Artin group case it is related to the embedding into a right-angled Coxeter group described by Davis and Januszkiewicz. We compare the approaches and also adapt the argument that the action extends to finite index supergroup that is a graph product of finite groups.
On the automorphisms of a graph product of abelian groups
Mauricio Gutierrez,Adam Piggott,Kim Ruane
Mathematics , 2007,
Abstract: We study the automorphisms of a graph product of finitely-generated abelian groups W. More precisely, we study a natural subgroup Aut* W of Aut W, with Aut* W = Aut W whenever vertex groups are finite and in a number of other cases. We prove a number of structure results, including a semi-direct product decomposition of Aut* W in which one of the factors is Inn W. We also give a number of applications, some of which are geometric in nature.
The automorphism group of the free group of rank two is a CAT(0) group
Adam Piggott,Kim Ruane,Genevieve S. Walsh
Mathematics , 2008,
Abstract: We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.
The automorphism group of a graph product with no SIL
Ruth Charney,Kim Ruane,Nathaniel Stambaugh,Anna Vijayan
Mathematics , 2009,
Abstract: We study the automorphisms of graph products of cyclic groups, a class of groups that includes all right-angled Coxeter and right-angled Artin groups. We show that the group of automorphism generated by partial conjugations is itself a graph product of cyclic groups providing its defining graph does not contain any separating intersection of links (SIL). In the case that all the cyclic groups are finite, this implies that the automorphism group is virtually CAT(0); it has a finite index subgroup which acts geometrically on a right-angled building.
Recognizing Right-Angled Coxeter Groups Using Involutions
Charles Cunningham,Andy Eisenberg,Adam Piggott,Kim Ruane
Mathematics , 2014,
Abstract: We consider the question of determining whether a given group (especially one generated by involutions) is a right-angled Coxeter group. We describe a group invariant, the involution graph, and we characterize the involution graphs of right-angled Coxeter groups. We use this characterization to describe a process for constructing candidate right-angled Coxeter presentations for a given group or proving that one cannot exist. We provide some first applications. In addition, we provide an elementary proof of rigidity of the defining graph for a right-angled Coxeter group. We also recover a result stating that if the defining graph contains no SILs, then Aut^0(W) is a right-angled Coxeter group.
$\mathrm{CAT}(0)$ Extensions of Right-angled Coxeter Groups
Charles Cunningham,Andy Eisenberg,Adam Piggott,Kim Ruane
Mathematics , 2015,
Abstract: We show that any split extension of a right-angled Coxeter group $W_{\Gamma}$ by a generating automorphism of finite order acts faithfully and geometrically on a $\mathrm{CAT}(0)$ metric space.
The effect of alternative mating designs and selection strategies on adult multiple ovulation and embryo transfer (MOET) nucleus breeding schemes in dairy cattle
J Ruane
Genetics Selection Evolution , 1991, DOI: 10.1186/1297-9686-23-1-47
Weavers & Warriors? Gender and Online Identity in 1997 and 2007 V1.0
Deirdre Ruane
Transforming Cultures , 2008,
Abstract: In 1997 the Internet was seen by many as a tool for radical reinterpretation of physicality and gender. Cybertheorists predicted we would leave our bodies behind and interact online as disembodied minds, and that the technology would reshape the way we saw ourselves. However, physicality has proved to be an inextricable part of all our interactions. Changing Internet technology has allowed Net users to find a myriad ways to perform and express their gender online. In this paper I consider attitudes to gender on the Net in 1997, when the main concerns were the imbalance between men and women online and whether it was possible or desirable to bring the body into online interactions. In much of the discourse surrounding gender online, a simple binary was assumed to exist. I go on to consider the extent to which those attitudes have changed today. Through my own experience of setting up a women’s community on Livejournal, and my observations of a men’s community set up in response, I conclude that though traditional attitudes to gender have largely translated to the Net and the binary is still the default view, some shifts have occurred. For example, between 1997 and today there seems to have been a fundamental change in perceptions of women’s attitudes to adversarial debate, and an increase in awareness of genders beyond the binary. In addition, experience and preliminary investigation lead me toward a hypothesis that today’s female-identified Net users are engaged in more conscious and active exploration and performance of their gender online than male-identified users are.
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