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Search Results: 1 - 10 of 223 matches for " Janko Latschev "
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Relative structure cycles and the existence of smooth Lyapunov 1-forms for flows
Janko Latschev
Mathematics , 2004,
Abstract: We give necessary and sufficient conditions for the existence of smooth Lyapunov 1-forms for the flow of a smooth vector field in terms of the behavior of certain locally finite invariant measures. The main statement generalizes a result of Schwartzman, whereas the methods are adapted from work of Sullivan.
Fukaya's work on Lagrangian embeddings
Janko Latschev
Mathematics , 2014,
Abstract: This is an expository account of some applications of string topology to the study of Lagrangian embeddings into symplectic manifolds, originally due to Fukaya, which was written as a contribution to a book on free loop spaces.
The role of string topology in symplectic field theory
Kai Cieliebak,Janko Latschev
Mathematics , 2007,
Abstract: We outline a program for incorporating holomorphic curves with Lagrangian boundary conditions into symplectic field theory, with an emphasis on ideas, geometric intuition, and a description of the resulting algebraic structures.
Algebraic Torsion in Contact Manifolds
Janko Latschev,Chris Wendl
Mathematics , 2010, DOI: 10.1007/s00039-011-0138-3
Abstract: We extract a nonnegative integer-valued invariant, which we call the "order of algebraic torsion", from the Symplectic Field Theory of a closed contact manifold, and show that its finiteness gives obstructions to the existence of symplectic fillings and exact symplectic cobordisms. A contact manifold has algebraic torsion of order zero if and only if it is algebraically overtwisted (i.e. has trivial contact homology), and any contact 3-manifold with positive Giroux torsion has algebraic torsion of order one (though the converse is not true). We also construct examples for each nonnegative k of contact 3-manifolds that have algebraic torsion of order k but not k - 1, and derive consequences for contact surgeries on such manifolds. The appendix by Michael Hutchings gives an alternative proof of our cobordism obstructions in dimension three using a refinement of the contact invariant in Embedded Contact Homology.
Compactness for holomorphic curves with switching Lagrangian boundary conditions
Kai Cieliebak,Tobias Ekholm,Janko Latschev
Mathematics , 2009,
Abstract: We prove a compactness result for holomorphic curves with boundary on an immersed Lagrangian submanifold with clean self-intersection. As a consequence, we show that the number of intersections of such holomorphic curves with the self-intersection locus is uniformly bounded in terms of the Hofer energy.
The Gromov width of 4-dimensional tori
Janko Latschev,Dusa McDuff,Felix Schlenk
Mathematics , 2011, DOI: 10.2140/gt.2013.17.2813
Abstract: We show that every 4-dimensional torus with a linear symplectic form can be fully filled by one symplectic ball. If such a torus is not symplectomorphic to a product of 2-dimensional tori with equal sized factors, then it can also be fully filled by any finite collection of balls provided only that their total volume is less than that of the 4-torus with its given linear symplectic form.
Homological algebra related to surfaces with boundary
Kai Cieliebak,Kenji Fukaya,Janko Latschev
Mathematics , 2015,
Abstract: In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic structure for all three contexts is a homotopy version of involutive bi-Lie algebras, which we call IBL$_\infty$-algebras,
Representations of content: psychological foundations and didactical background
Tomá? Janko
Pedagogicka Orientace , 2012,
Abstract: This theoretical study concerns the issue of representations. Representation is a concept used when analysing and explaining human perception, cognition, communication, and learning. Firstly, we introduce the psychological foundations of the concept. Secondly, we clarify the concept of representations and its division in cognitive psychology. We define two basic forms of external representations - verbal and visual. In social psychology, the concept is used for explaining of how much individual cognition is determined by socio-cultural factors. Further, we mention the concept of representations that draws on the Theory of social representations (Moscovici) and Vygotsky's ideas. The author seeks to develop a concept of representations usable in didactic discourse. The importance of representations for content-oriented didactics is clarified. We also define the levels on which a teacher reasons when using representations during instruction. Representations of curricular content, which are believed to play an important role when presenting the content to students, are also mentioned.
Epitaphios of Jovan, the Metropolitan of Skopje, in the treasury of the Hilandar monastery
Radovanovi? Janko
Zograf , 2006, DOI: 10.2298/zog0731169r
Abstract: The epitaphios of Jovan, the Metropolitan of Skopje, was created between 1346 and 1348. It is unique for its beauty and iconographic program and, at the same time, it is the oldest of the epitaphia preserved in our country. The epitaphios was worn in the course of Holy Liturgy, during the Great Entrance in the cathedral churches and the major monasteries. Metropolitan Jovan presented the epitaphios as a gift to Christ 'my life-giver.' Depicted on its central field is the Epitaphios Threnos (Lamentation at the Tomb). Added around it, at a later time it seems, are bands representing the fourteen scenes of Great Feasts and the officiating Church Fathers, in embroidery. Holy Liturgy is served by the greatest fathers and teachers of the Church and Metropolitan Jovan.
A teratological motif in the ceramoplastic decoration of the Virgin Ljevi ka in Prizren: Iconology of apsidal three-light window
Maglovski Janko
Zograf , 2004, DOI: 10.2298/zog0530119m
Abstract: The author draws attention to two ceramoplastic details, symmetrical in relation to the vertical axis of apsidal three-light window, created at the ends of the band of a series of identical ceramoplastic patterns. Those details were recognized in earlier literature as "two small fish" of baked clay and are considered to be a unique example of this kind of motive in ceramoplastic decoration in Byzantine architecture, and in architecture inspired by it. The author advocates the verbal definition of the image and indicates that the said details can scarcely be described as fish. He finds a new matrix, to which the images correspond, in the linearly depicted heads of snake-like and dragon-like monsters that appear in the repertoire of teratological ornamentation. The author indicates that the altar window of the church of Virgin Ljevi ka in Prizren is encircled by a double asp, a symbol of the evil of this world. He stresses that the design of this altar window is divided into two areas in the iconological sense like the western portals in Studenica and De ani The external represents this sinful world and the internal, symbolized by the victory cross of Christ (IG XC NH Kfl) represents the community of the faithful in Christ, i.e. the side of good. A comparison is drawn for the first time in the text, between the ceramoplastic decoration on the fa ade of the church and the teratological ornamentation on the pages of the book.
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