1,721,028 research outputs found
L2-torsion of Hyperbolic Manifolds of Finite Volume
No full textSuppose M¯ is a compact connected odd-dimensional manifold with boundary, whose interior M comes with a complete hyperbolic metric of finite volume. We will show that the L2-topological torsion of M¯ and the L2-analytic torsion of the Riemannian manifold M are equal. In particular, the L2-topological torsion of M¯ is proportional to the hyperbolic volume of M, with a constant of proportionality which depends only on the dimension and which is known to be nonzero in odd dimensions [HS]. In dimension 3 this proves the conjecture [Lü2, Conjecture 2.3] or [LLü, Conjecture 7.7] which gives a complete calculation of the L2-topological torsion of compact L2-acyclic 3-manifolds which admit a geometric JSJT-decomposition.¶In an appendix we give a counterexample to an extension of the Cheeger-Müller theorem to manifolds with boundary: if the metric is not a product near the boundary, in general analytic and topological torsion are not equal, even if the Euler characteristic of the boundary vanishes
Positive scalar curvature due to the cokernel of the classifying map
Full text linkThis paper contributes to the classification of positive scalar curvature metrics up to bordism and up to concordance. Let M be a closed spin manifold of dimension ≥ 5 which admits a metric with positive scalar curvature. We give lower bounds on the rank of the group of psc metrics over M up to bordism in terms of the corank of the canonical map KO*(M) → KO*(Bπ1(M)), provided the rational analytic Novikov conjecture is true for π1(M)
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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
Bordism, rho-invariants and the Baum–Connes conjecture
No full textLet � be a finitely generated discrete group. In this paper we establish vanishing results for rho-invariants associated to (i) the spin Dirac operator of a spin manifold with positive scalar curvature and fundamental group�; (ii) the signature operator of the disjoint union of a pair of homotopy equivalent oriented manifolds with fundamental group�. The invariants we consider are more precisely the Atiyah–Patodi–Singer ( APS) rho-invariant associated to a pair of finite dimensional unitary representations 1; 2W � ! U.d/, theL 2-rho-invariant of Cheeger–Gromov, the delocalized eta-invariant of Lott for a non-trivial conjugacy class of � which is finite. We prove that all these rho-invariants vanish if the group � is torsion-free and the Baum–Connes map for the maximal group C*-algebra is bijective. This condition is satisfied, for example, by torsion-free amenable groups or by torsion-free discrete subgroups of SO.n;1 / and SU.n;1/. For the delocalized invariant we only assume the validity of the Baum–Connes conjecture for the reduced C*-algebra. In addition to the examples above, this condition is satisfied e.g. by Gromov hyperbolic groups or by cocompact discrete subgroups of SL.3; C/. In particular, the three rho-invariants associated to the signature operator are, for such groups, homotopy invariant. For the APS and the Cheeger–Gromov rho-invariants the latter result had been established by Navin Keswani. Our proof reestablishes this result and also extends it to the delocalized eta-invariant of Lott. The proof exploits in a fundamental way results from bordism theory as well as various generalizations of the APS-index theorem; it also embeds these results in general vanishing phenomena for degree zero higher rho-invariants (taking values inA=ŒA;A � for suitable C*-algebrasA). We also obtain precise information about the eta-invariants in question themselves, which are usually much more subtle objects than the rho-invariants
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe 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
Groups with torsion, bordism and rho invariants
Full text linkLet Γ be a discrete group, and let M be a closed spin manifold of dimension m> 3 with π1(M) = Γ. We assume that M admits a Riemannian metric of positive scalar curvature. We discuss how to use the L 2-rho invariant ρ(2) and the delocalized eta invariant η<g> associated to the Dirac operator on M in order to get information about the space of metrics with positive scalar curvature. In particular we prove that, if Γ contains torsion and m ≡ 3 (mod 4) then M admits infinitely many different bordism classes of metrics with positive scalar curvature. This implies that there exist infinitely many concordance classes; we show that this is true even up to diffeomorphism. If Γ has certain special properties, e.g. if it contains polynomially growing conjugacy classes of finite order elements, then we obtain more refined information about the “size ” of the space of metric of positive scalar curvature, and these results also apply if the dimension is congruent to 1 mod 4. For example, if dim(M) ≡ 1 (mod 4) and Γ contains a central element of odd order, then the moduli space of metrics of positive scalar curvature (modulo the action of the diffeomorphism group) has infinitely many components, if it is not empty. Some of our invariants are the delocalized η-invariants introduced by John Lott. These invariants are defined by certain integrals whose convergence is not clear in general, and we show, in effect, that examples exist where this integral definitely does not converge, thus answering a question of Lott. We also discuss the possible values of the rho invariants of the Dirac operator and show that there are certain global restrictions (provided the scalar curvature is positive)
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