1,720,962 research outputs found
A geometric approach to equivariant factorization homology and nonabelian Poincar\'e duality
Get PDFFix a finite group G and an n-dimensional orthogonal G-representation V. We
define the equivariant factorization homology of a V-framed smooth G-manifold
with coefficients in an -algebra using a two-sided bar construction,
generalizing [And10, KM18]. This construction uses minimal categorical
background and aims for maximal concreteness, allowing convenient proofs of key
properties, including invariance of equivariant factorization homology under
change of tangential structures. Using a geometrically-seen scanning map, we
prove an equivariant version (eNPD) of the nonabelian Poincare duality theorem
due to several authors. The eNPD states that the scanning map gives a
G-equivalence from the equivariant factorization homology to mapping spaces out
the one-point compactification of the G-manifolds when the coefficients are
G-connected. For non-G-connected coefficients, when the G-manifolds have
suitable copies of R in them, the scanning map gives group completions. This
generalizes the recognition principle for V -fold loops spaces in [GM17].Comment: 46 pages; major changes from version 1, including rewriting the
introduction and adding new sections 3.4 and 4.
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A Geometric Approach to Equivariant Factorization Homology and Nonabelian Poincaré Duality
Get PDFFactorization homology is a homology theory on manifolds with coefficients in suitable -algebras. In this paper, we use the minimal categorical background and maximal concreteness to study equivariant factorization homology in the -framed case.
We work with a finite group and an -dimensional orthogonal -representation . The main results are:
\begin{enumerate}
\item We construct a -enriched category . Its objects are -framed -manifolds of dimension . The endomorphism operad of the object is equivalent to the little -disk operad.
\item With this category, we define the equivariant factorization homology by a monadic bar construction.
\item We prove the nonabelian Poincar\'e duality theorem using a geometrically-seen scanning map, which establishes a weak -equivalence between and .
\end{enumerate}
Here, is a -framed manifold, and is its one-point compactification. In the language of Guillou-May \cite{GM17}, the coefficient is an algebra over the little -disks operad and is the -fold deloop of
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
Equivariant Complex Cobordism and Geometric Orientations
No full textWe calculate the cobordism ring of stably almost complex manifolds with involution, and investigate the equivariant spectrum which represents it. We introduce the notion of geometrically oriented spectra, which extends the notion of complex oriented spectra, and of which the geometric cobordism spectrum is the universal example. Other examples of geometrically oriented spectra include the Eilenberg-Maclane spectrum associated to a constant Mackey functor, and the connective cover of equivariant complex K theory. On the algebraic side, we define and study filtered equivariant formal group laws, which are the algebraic structures determined by geometrically oriented spectra. We prove some of the fundamental properties of filtered equivariant formal group laws, as well as a universality statement for the filtered equivariant formal group law determined by the geometric complex cobordism spectrum.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/174599/1/jackcar_1.pd
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
Equivariant orientation of vector bundles over disconnected base spaces
Get PDFIn this paper, we view the equivariant orientation theory of equivariant vector bundles from the lenses of equivariant Picard spectra. This viewpoint allows us to identify, for a finite group , a precise condition under which an -orientation of a -equivariant vector bundle is encoded by a Thom class. Consequently, we are able to construct a generalization of the first StiefelWhitney class of a homogeneous -equivariant bundle with respect to an -ring spectrum . As an application, we show that the -fold direct sum of any homogeneous bundle is -orientable, where is the Burnside Mackey functor. We notice that -orientability is equivalent to -orientability when the order of is odd. When the order of is even, we show that a -equivariant analog of the tautological line bundle over is -orientable but not -orientable.24 page
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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