1,721,113 research outputs found
Dimension of elementary amenable groups
No full textThis paper has three parts. It is conjectured that for every elementary amenable group G and every non-zero commutative ring k, the homological dimension hdk(G)is equal to the Hirsch length h(G) whenever G has no k-torsion. In Part I this conjecture is proved for several classes, including the abelian-by-polycyclic groups. In Part II it is shown that the elementary amenable groups of homological dimension one are colimits of systems of groups of cohomological dimension one. In Part III the deep problem of calculating the cohomological dimension of elementary amenable groups is tackled with particular emphasis on the nilpotent-by-polycyclic case, where a complete answer is obtained over Q for countable group
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Profinite rigidity of group extensions
Get PDFThis thesis investigates the extent to which finite quotients can distinguish between non-isomorphic groups G sharing a fixed normal subgroup N and a fixed quotient Q ∼= G/N. We generally assume that Q and N are finitely generated and that Q is good in the sense of Serre. Two broad themes in this study are profinite conjugacy of outer actions and collapsing of cohomology orbits, which we explore across various contexts.
First, we construct large families of profinitely conjugate outer actions φi: F2 → Out(N) for N a free group, a surface group, or a free abelian group of sufficiently large finite rank. These lead to infinite families of groups of the form N ⋊ F2 sharing the same finite quotients.
Second, we investigate both themes in crystallographic groups, providing a detailed analysis of examples from the literature and presenting new ones, including a pair of non-isomorphic crystallographic groups in dimension 8 that share the same finite quotients.
Third, we extend Wilkes’ results on the profinite rigidity of Seifert fibre spaces to central extensions of 2-orbifold groups with higher-rank centre. We prove that both rigid and non-rigid phenomena occur and that within this family G1 and G2 share the same finite quotients if and only if G1 × Z ∼= G2 × Z.
Fourth, we prove that finitely generated free-by-cyclic groups with centre are all distinguished from each other by their finite quotients. We do this proving a new result that Fn-by-(Z /m) groups are uniquely determined by a poset that records the conjugacy classes of their finite subgroups, the sizes of these subgroups and the first Betti number of their centralisers
Constructions in stable commutator length and bounded cohomology
Get PDFThe bounded cohomology of a group G with coefficients in
a normed G-module V was first systematically studied by Gromov in
1982 in his seminal paper [Gro82] in connection to the minimal volume of manifolds. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly
compute bounded cohomology, even for the most basic groups: There is no finitely generated group G for which the full bounded cohomology with real coefficients is known except where it is known
to vanish in all degrees (see [Mon06]). In this thesis we discuss several new constructions for classses in bounded cohomology.
There is a well-known interpretation of ordinary group cohomology in
degrees 2 and 3 in terms of group extensions. We establish an analogous interpretation in the context of bounded cohomology. This involves certain maps between arbitrary groups called quasihomomorphisms, which were defined and studied by Fujiwara and Kapovich in [FK16].
A key open problem is to compute the full bounded cohomology of a non-abelian free group F with trivial real coefficients. It is known that the bounded cohomology in dimension n is trivial for n = 1 and infinite dimensional for n = 2, 3, but essentially nothing is known about for n ⥠4. For n = 4, one may construct classes by taking the cup product between two 2-classes, but it is
possible that all such cup-products are trivial. We show that all such
cup-products do indeed vanish if both classes are induced by the
quasimorphisms of Brooks or Rolli.</p
Asymptotic invariants of infinite discrete groups
Get PDFAsymptotic cones. A finitely generated group has a word metric, which one can scale and thereby view the group from increasingly distant vantage points. The group coalesces to an "asymptotic cone" in the limit (this is made precise using techniques of non-standard analysis). The reward is that in place of the discrete group one has a continuous object "that is amenable to attack by geometric (e.g. topological, infinitesimal) machinery" (to quote Gromov). We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions concerning filling N-spheres in an appropriately coarse sense. We interpret the criteria in the case where X is a finitely generated group Γ with a word metric. This leads to upper bounds on filling functions for groups with simply connected cones -- in particular they have linearly bounded filling length functions. We prove that if all the asymptotic cones of Γ are N-connected then Γ is of type FN+1 and we provide N-th order isoperimetric and isodiametric functions. Also we show that the asymptotic cones of a virtually polycyclic group Γ are all contractible if and only if Γ is virtually nilpotent. Combable groups and almost-convex groups. A combing of a finitely generated group Γ is a normal form; that is a choice of word (a combing line) for each group element that satisfies a geometric constraint: nearby group elements have combing lines that fellow travel. An almost-convexity condition concerns the geometry of closed balls in the Cayley graph for Γ. We show that even the most mild combability or almost-convexity restrictions on a finitely presented group already force surprisingly strong constraints on the geometry of its word problem. In both cases we obtain an n! isoperimetric function, and upper bounds of ~ n2 on both the minimal isodiametric function and the filling length function
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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