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On the Plumbing Structure of Fibre Surfaces
Full text linkThis thesis is situated in the mathematical field of low-dimensional topology and is concerned with a particular class of knots and links known as fibred links. A link L in the three-sphere is fibred if its complement admits a fibration over the circle with fibres the interiors of Seifert surfaces for L. These surfaces, called fibre surfaces, are our main objects of study. For example, all torus links and all positive braid links are fibred. The simplest example of a fibred link is the Hopf link; its fibre surface is an annular band with a full twist. Using a geometric operation called plumbing, Hopf bands can be glued together so as to form more complicated fibre surfaces. The reverse operation, deplumbing, consists in removing a Hopf band from a fibre surface. It amounts to cutting that fibre surface along a proper arc.
By a theorem of Giroux and Goodman's, every fibre surface has a plumbing structure: it can be obtained from the standard disk by plumbing and deplumbing some number of Hopf bands. Our main results concern the (non-)uniqueness of the plumbing structure of a given fibre surface. Specifically, we study the cases of torus links and positive arborescent Hopf plumbings. Among these, we characterise the links arising from simple plane curve singularities by the finiteness of proper arcs that correspond to deplumbing a Hopf band
Cutting Arcs For Torus Links And Trees
No full textAmong all torus links, we characterise those arising as links of simple plane curve singularities by the property that their fibre surfaces admit only a finite number of cutting arcs that preserve fibredness. The same property allows a characterisation of Coxeter-Dynkin trees (i.e., An , Dn , E6 , E7 and E8 ) among all positive tree-like Hopf plumbings
The bridge number of arborescent links with many twigs
Full text linkWe prove the meridional rank conjecture for arborescent links associated to plane trees with the following property: all branching points carry a straight branch to at least three leaves. The proof involves obtaining an upper bound on the bridge number in terms of the maximal number of link components of the underlying tree, which is valid for all arborescent links
On the stabilization height of fiber surfaces in S³
No full textThe stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We show
that families of fibre surfaces related by iterated Stallings twists have unbounded stabilisation height
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
HOPF BANDS IN ARBORESCENT HOPF PLUMBINGS
Full text linkFor a positive Hopf plumbed arborescent Seifert surface S , we study the set of Hopf bands H ⊂ S , up to homology and up to the action of the monodromy. The classification of Seifert surfaces for which this set is finite is closely related to the classification of finite Coxeter groups
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