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The topology of Stein fillable manifolds in high dimensions II
Get PDFWe continue our study of contact structures on manifolds of dimension at least five using complex surgery theory. We show that in each dimension 2q+1 > 3 there are 'maximal' almost contact manifolds to which there is a Stein cobordism from any other (2q+1)-dimensional contact manifold. We show that the product M x S^2 admits a weakly fillable contact structure provided M admits a weak symplectic filling (W, \omega) with \omega(\pi _2(M))=0. We also study the connection between Stein fillability and connected sums: we give examples of almost contact manifolds for which the connected sum is Stein fillable, while the components are not.
Concerning obstructions to Stein fillings, we show that the (8k-1)-dimensional sphere has an almost contact structure which is not Stein fillable once k > 1. As a consequence we deduce that any highly connected almost contact (8k-1)-manifold (with k > 1) admits an almost contact structure which is not Stein fillable
Lefschetz Fibrations on 4-manifolds
No full textWe explicitly construct genus-2 Lefschetz fibrations whose total spaces are minimal symplectic 4-manifolds homeomorphic to complex rational surfaces for , and to for . Complementarily, we prove that there are no minimal genus-2 Lefschetz fibrations whose total spaces are homeomorphic to any other simply-connected 4-manifold with , with one possible exception when . Meanwhile, we produce positive Dehn twist factorizations for several new genus-2 Lefschetz fibrations with small number of critical points, including the smallest possible example, which follow from a reverse engineering procedure we introduce for this setting. We also derive exotic minimal symplectic 4-manifolds in the homeomorphism classes of and from small Lefschetz fibrations over surfaces of higher genera
The Upsilon invariant
No full textKnot Floer homology is a refinement of Heegaard Floer homology, providing an invariant for a pair (a 3-manifold, a knot in it). Recently, in collaboration with P. Ozsvath and Z. Szabo, we have found
a 1-parameter 'deformation' of knot Floer homology for knots in S^3, leading to a family of concordance invariants. For the value t=1 the deformation admits a further symmetry, providing a bound on the unoriented 4 ball genus (smooth crosscap number) of the knot at hand. In the lecture I plan to recall the basic constructions behind knot Floer homology, list its basic properties, and show how the deformation works. Using grid diagrams we will discuss a sketch of the proof of the genus bounds.Non UBCUnreviewedAuthor affiliation: Hungarian Academy of SciencesFacult
Knots in Lattice homology
No full textNon UBCUnreviewedAuthor affiliation: Hungarian Academy of SciencesFacult
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Topologie
Get PDFThe lectures in the workshop covered various topics in modern topology, including algebraic and geometric topology, homotopy theory, geometric group theory, and manifold topology, as well as connections to neighboring areas, most prominently symplectic topology/geometry. The following current research topics received more attention during the workshop: manifolds and K-theory, symplectic topology and Floer homology, generalizations of hyperbolic techniques in geometric group theory, and equivariant and motivic homotopy theory. The aim of the various topics was to foster communication and provide chances for participants to see and experience driving questions and important methods in nearby fields within the realm of topology
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
Topologie
No full textThe lectures in the workshop covered various topics in modern topology, including algebraic and geometric topology, homotopy theory, geometric group theory, and manifold topology, as well as connections to neighboring areas, most prominently symplectic topology/geometry. The following current research topics received more attention during the workshop: manifolds and K-theory, symplectic topology and Floer homology, generalizations of hyperbolic techniques in geometric group theory, and equivariant and motivic homotopy theory. The aim of the various topics was to foster communication and provide chances for participants to see and experience driving questions and important methods in nearby fields within the realm of topology
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
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