105,326 research outputs found
Diameter Bounds on the Complex of Minimal Genus Seifert Surfaces for Hyperbolic Knot
No full textGiven a link L in the 3-sphere, one can build simplicial complexes MS(L) and IS(L), called the Kakimizu complexes. These complexes have isotopy classes of minimal genus and incompressible Seifert surfaces for L as their vertex sets and have simplicial structures defined via a disjointness property. The Kakimizu complexes enjoy many topological properties and are conjectured to be contractible. Following the work of Gabai on sutured manifolds and Murasugi sums, MS(L) and IS(L) have been classified for various classes of links. This thesis focuses on hyperbolic knots; using minimal surface representatives and Kakimizu's formulation of the path-metric on MS(K), we are able to bound the diameter of this complex in terms of only the genus of the knot. The techniques of this paper are also generalized to one-cusped manifolds with a preferred relative homology class
Subgroup separability, knot groups, and graph manifolds
No full textThis paper answers a question of Burns, Karrass and Solitar by giving examples of knot and link groups which are not subgroup-separable. For instance, it is shown that the fundamental group of the square knot complement is not subgroup separable. We characterise the Graph Manifolds with subgroup separable fundamental group as precisely the geometric ones, i.e. the Seifert Fibered 3-manifolds and the Sol manifolds, and show that there is a specific non-subgroup separable group which is a subgroup in all other cases
The Seifert construction.
No full text<p>The construction of the <i>T</i><sub>2</sub>-tetrahedral link from a tetrahedral graph and the construction of <i>Seifert surface</i> based on its minimal projection. Each strand is assigned by a different color. The Seifert circles distributed at vertices have opposite direction with the Seifert circles distributed at edges. The arrows indicate the 5′ - 3′ direction of the DNA backbone.</p
Film and propaganda: an outline of film production in Slovenia until the end of the Second World War
No full textDiplomska naloga govori o razvoju filmske produkcije na Slovenskem, in sicer o samih začetkih, ko so prebivalci današnje Slovenije prvič videli gibljive slike, in o ustvarjalcih, ki so se naposled sami preizkusili v tej umetnosti in danes veljajo za začetnike slovenskega filma. Prvi metri slovenskega filma so nastali večinoma izpod rok fotoamaterjev in ljubiteljev filma. Posneti material hranijo večinoma v Arhivu Republike Slovenije in Narodnem muzeju v Ljubljani.
Delo je bilo usmerjeno različno, v arhive – film, knjige, članke in časopise, ki so izhajali skupaj z omenjenimi filmi. Med njimi izstopa časopis Slovenski narod, ki kaže, da je bil filmu tudi najbolj naklonjen, vsi ti časopisi so dostopni v Digitalni knjižnici Slovenije.
Diplomska naloga je razdeljena na tri dele. Prvo poglavje govori o začetkih kinematografije na Slovenskem in o njihovih akterjih, ki so bili najbolj zaslužni za njen razvoj. Opisuje domačo filmsko proizvodnjo do začetka druge svetovne vojne, od prvih metrov domačega filma, ki jih je posnel Karol Grossmann, do premier prvih dveh slovenskih celovečernih filmov in ustanovitve edine med vojno delujoče produkcije Emona film.
Drugi del se posveti propagandi, njeni teoriji in njeni vlogi v vojni oziroma v družbi. Na kratko se posveti tudi okupatorjevi propagandi. Osredotoča se predvsem na delovanje Emona filma in na njen izdelek Partizanski dokumenti, ki so danes pomemben vir za vpogled v medvojno produkcijo dokumentarnega filma oziroma propagande na Slovenskem. Poleg omenjenega podjetja opiše tudi delovanje filmske sekcije NOB, ki je bila poleg Emona filma tudi edina, ki je snemala v času vojne.
V zadnjem delu naloga na kratko opiše nadaljevanje filmske produkcije iz časa NOB, se naveže na povojno filmsko produkcijo, išče v njej sledi vojne in vpliv le-te na življenje po njej.The thesis deals with the development of film production in Slovenia, namely about the very beginnings, when the inhabitants of modern-day Slovenia saw motion pictures for the first time, and about the creators who eventually tested themselves in this art and are today considered the pioneers of Slovenian cinema. The first meters of Slovenian film were mostly created by amateurs and film lovers. The recorded material is kept mostly in the Archives of the Republic of Slovenia and the National Museum in Ljubljana.
Work took different directions, to the archives - film, books, articles and newspapers, which were published together with the mentioned films. Among them, the newspaper Slovenski narod stands out in that it was the most favorable to the film. All of these newspapers are available in the Digital Library of Slovenia.
The thesis is divided into three parts. The first chapter talks about the beginnings of cinematography in Slovenia and the people who were most responsible for its development. It describes domestic film production until the beginning of the Second World War, from the first meters of domestic film shot by Karol Grossmann, to the premieres of the first two Slovenian feature films and the establishment of the only production company operating during the war, Emona film.
The second part is devoted to propaganda, its theory and its role in war, or rather, society. It also briefly addresses the occupier\u27s propaganda, but mainly it focuses on the operation of Emona film and its product Partizanski dokumenti, which today are an important source for insight into the interwar production of documentary films or propaganda in Slovenia. In addition to the aforementioned company, it also deals with the operation of the NOB (national liberation struggle) film section, which, apart from Emona film, was also the only one that filmed during the war.
In the final part, the thesis briefly describes the continuation of film production from the NOB period, moves on to post-war film production, looks for traces of the war and its impact on life thereafter
Hopf plumbing, arborescent Seifert surfaces, baskets, espaliers, and homogeneous braids
No full textAbstractFour constructions of Seifert surfaces—Hopf and arborescent plumbing, basketry, and T-bandword handle decomposition—are described, and some interrelationships expounded, e.g., arborescent Seifert surfaces are baskets; Hopf-plumbed baskets are precisely homogeneous T-bandword surfaces
Homogeneous links and the Seifert matrix
No full textHomogeneous links were introduced by Peter Cromwell, who pr oved that the projection surface of these links, that given by the Seifert al- gorithm, has minimal genus. Here we provide a different proof , with a geometric rather than combinatorial flavor. To do this, we fir st show a direct relation between the Seifert matrix and the decompo sition into blocks of the Seifert graph. Precisely, we prove that the Sei fert matrix can be arranged in a block triangular form, with small boxes in th e diagonal corresponding to the blocks of the Seifert graph. Then we pro ve that the boxes in the diagonal has non-zero determinant, by looking a t an explicit matrix of degrees given by the planar structure of the Seifer t graph. The paper contains also a complete classification of the homogen eous knots of genus one
Construction of Seifert surfaces by differential geometry
No full textA Seifert surface for a knot in ℝ³ is a compact orientable surface whose boundary is the knot. Seifert surfaces are not unique. In 1934 Herbert Seifert provided a construction of such a surface known as the Seifert Algorithm, using the combinatorics of a projection of the knot onto a plane. This thesis presents another construction of a Seifert surface, using differential geometry and a projection of the knot onto a sphere. Given a knot K : S¹⊂ R³, we construct canonical maps F : ΛdiffS² → ℝ=4πZ and G : ℝ³ - K(S¹) → ΛdiffS² where ΛdiffS² is the space of smooth loops in S². The composite FG : ℝ³ - K(S¹) → ℝ=4πZ is a smooth map defined for each u∈2 ℝ³ - K(S¹) by integration of a 2- form over an extension D² → S² of G(u) : S1 → S². The composite FG is a surjection which is a canonical representative of the generator 1∈H¹(ℝ³- K(S¹)) = Z. FG can be defined geometrically using the solid angle. Given u ∈ ℝ³ - K(S¹), choose a Seifert surface Σu for K with u ∉ Σu. It is shown that FG(u) is equal to the signed area of the shadow of Σu on the unit sphere centred at u. With this, FG(u) can be written as a line integral over the knot. By Sard's Theorem, FG has a regular value t ∈ ℝ=4πZ. The behaviour of FG near the knot is investigated in order to show that FG is a locally trivial fibration near the knot, using detailed differential analysis. Our main result is that (FG)-¹(t)⊂ ℝ³ can be closed to a Seifert surface by adding the knot
The integral homology of orientable Seifert manifolds
No full textAbstractFor any orientable Seifert manifold M, the integral homology group H1(M)=H1(M;Z) is computed and explicit generators are found. This calculation gives a presentation for the p-torsion of H1(M) for any prime p. Since Seifert manifolds have dimension 3, H1(M) determines H∗(M;A) and H∗(M;A) as well, for any abelian group A. The complete details are given when A=Z, Z/ps.In order to calculate the partition functions of the Dijkgraaf–Witten topological quantum field theories it is necessary to compute the linking form of the underlying 3-manifold. In the case of the orientable Seifert manifolds it is possible to compute the linking form. The calculation of the linking form involves finding a presentation of the torsion of the first integral homology of the orientable Seifert manifolds, which is the main result of this paper
Seifert fibered spaces: triangulation and recognition
No full textIn this thesis, we study 3-manifolds from an algorithmic point of view. Our motivation is the conjecture that 3-manifold homeomorphism is in NP. The hope is that if one can prove this conjecture in the special case of geometric 3-manifolds, then one can use geometrisation to prove the general statement. This thesis predominantly concerns itself with the Seifert fibered case.
The idea is to show that we can bound the size of characteristic topological structures in an arbitrary triangulation. To that end, we first study the size of minimal triangulations of Seifert fibered spaces. We show that we can realise certain important curves, the singular fibres, as subcomplexes by increasing the size of an arbitrary triangulation by a linear factor. We use this result to give bounds on the triangulation complexity of Seifert fibered spaces with non-empty boundary, which is the minimum number of tetrahedra in a triangulation of a manifold. We give a formula for the triangulation complexity which is correct up to a multiplicative factor. We also give an optimal bound for the triangulation complexity of a connect sum.
We then turn our attention to the 3-manifold homeomorphism problem. We first show that recognising (closed) Euclidean and Nil 3-manifolds, and deciding if a given set of Seifert data is correct for them, is in NP. We then consider the case of recognising Seifert fibered spaces with non-empty boundary. We prove that the recognition problem for Seifert fibered spaces with non-empty boundary is in NP, and that deciding whether a given Seifert fibered space with non-empty boundary admits certain Seifert data is in NP ∩ co-NP. To do this, we give bounds on the size of a complete collection of normal annuli in such a Seifert fibered space. The technique we use for this bound, which is the theory of normal surfaces in split handle structures, comprises half this chapter and can be used generally to give a bound of the form c|T|² on the weight of a complete collection of (disjoint) incompressible normal surfaces in an arbitrary triangulation T
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Knots with infinitely many incompressible Seifert surfaces
No full textWe show that a knot in with an infinite number of distinct incompressible
Seifert surfaces contains a closed incompressible surface in its complement
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