Low dimensional topology

FROM THE BACK COVER: What is the essential nature of meaning? . . . . . This book answers by examining interpretive theories from the past and present. It finds that an historical struggle with meaning has been underway since the Reformation, a struggle that reaches crisis proportions in the 20th century. On the one hand, this crisis is mollified by Heidegger's hermeneutical phenomenology, which argues that we are always already in a meaningful relationship to the objects of the world. On the other hand, this crisis is exacerbated when phenomenology, structuralism, and aesthetic theory directly make meaning into an object of study. . . . . . . . . These historical developments culminate with the psychoanalyst Jacques Lacan, whose non-hermeneutical phenomenology delimits a cause of meaning said to be closely linked to the core of subjectivity. Intriguingly, Lacan's work reveals meaning to be sexual in nature. By integrating his notion of sexual difference with his work in discourse theory and topology, this book demonstrates how the subject's struggle with meaning can be suspended.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GENERAL DESCRIPTION: Broadly speaking, the majority of books on Jacques Lacan focus on the earlier periods of his career. They also tend to target the psychoanalytic clinical community, or else discuss his work in various political, social, and cultural contexts. But in almost all cases these books refrain from a detailed exegesis of his actual texts. They instead prefer to comment on his theoretical apparatus as a whole before turning to its practical implications. . . . . . This book positions itself against this grain. Firstly, it closely analyzes some half-dozen key Lacanian texts. This analysis is organized under a single thematic – the question of meaning – in order to advance the reader's understanding of the trajectory of Lacan's thought across his entire career, as well as to promote the book's thesis that the field of meaning can be suspended. Accordingly, an initial chapter takes up the hermeneutical tradition from Flacius onward. This is then supplemented by a chapter which surveys phenomenological, structuralist and aesthetic theories of meaning and their differing methods of textual analysis. Together these two chapters provide a unique context for the sustained analysis of Lacan's texts which begins in the third chapter, an analysis that forms the bulk of the book's content. This contextualization potentially widens the book's appeal to any scholar wishing to explore his relationship to those textual objects he interacts with on a daily basis. And because this book assumes the reader has little to no familiarity with Lacan, the reader will find patient explanations of the basics of his theories before slowly being led up to the more difficult theories of his late years. Again the argument is that Lacan has something to offer all scholars. His work is not just reserved for psychoanalysts. . . . . . It is with his late theories that the serious student of Lacan will find the book's most original contribution. For in the fourth chapter a detailed account is provided of how Lacan derived his infamous formulae of sexuation from Aristotelian logic. These formulae are then extensively discussed against the backdrop of interpretive theory and textual analysis, showing how these formulae capture much more than just the difference between the sexes. Strikingly, this difference is also found to run through meaning itself, something the final chapter aims to demonstrate. It does this by amalgamating three key components of late-Lacan: sexuation, discourse theory and his use of topological spaces. This amalgamation is a first in the literature. But this amalgamation is not just useful in demonstrating the book's thesis. It further suggests how seemingly divergent aspects of late-Lacanian theory can be made to work together.

"ABSTRACT:
    This study assumes the subject's pursuit of meaning is generally incapacitating and should be suspended. It aims to demonstrate how such a suspension is theoretically accomplished by utilizing Lacan's formulae of sexuation integrated with his work in discourse theory and topology.
    Part I places this study into context by examining scholarship from the established fields of hermeneutics, phenomenology, (post)structuralism, aesthetic theory and psychoanalysis in order to extract out their respective theory of meaning. These theories reveal that an historical struggle with meaning has been underway since the Reformation and reaches near crisis proportions in the 20th century. On the one hand this crisis is mollified by the rise of Heideggerian-Gadamerian hermeneutical phenomenology which questions traditional epistemological approaches to the text using a new ontological conceptualization of meaning and a conscious rejection of methodology. On the other hand this crisis is exacerbated when the ubiquitous nature of meaning is itself challenged by (post)structuralism's discovery of the signifier which inscribes a limit to meaning, and by the domains of sense and nonsense newly opened up by aesthetic theory. These historical developments culminate in the field of psychoanalysis which most consequentially delimits a cause of meaning said to be closely linked to the core of subjectivity.
    Part II extends these findings by rigorously constructing out of the Lacanian sexuated formulae a decidedly non-hermeneutical phenomenological approach useful in demonstrating the sexual nature of meaning. Explicated in their static state by way of an account of their original derivation from the Aristotelian logical square, it is argued that these four formulae are relevant to basic concerns of textual theory inclusive of the hermeneutical circle of meaning. These formulae are then set into motion by integrating them with Lacan's four discourses to demonstrate the breakdown of meaning. Finally, the cuts and sutures of two-dimensional space that is topology as set down in L'étourdit are performed to confirm how the very field of meaning is ultimately suspended from a nonsensical singular point known in Lacanian psychoanalysis as objet a. The contention is that by occupying this point the subject frees himself from the debilitating grip of meaning."

Nickel nanoparticles arrays, growth into hydro-genated amorphous carbon, were prepared by means of RF-plasma enhanced chemical vapor deposition and RF-sputtering co-deposition from acetylene and a nickel target. The resulting nanocomposite films were characterized by X-ray diffraction and atomic force microscopy, and their magnetic responses and magnetoresistance behavior were investigated as a function of the exciting magnetic field and the Ni nanoparticles content, which was conveniently controlled by adjusting the deposition time. These physical properties were explained by a combination of hopping and tunneling effects.

We introduce symplectic structures on Lie pairs of (real or complex) algebroids as studied by Chen, Stiénon and the second author, encompassing homogeneous symplectic spaces, symplectic manifolds with a 𝔤-action and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky-Witten-type invariants of three-manifolds and knots, given respectively by weight systems on trivalent and chord diagrams.

Rafi and Schleimer recently proved that the natural relation between curve complexes induced by a covering map between two surfaces is a quasi-isometric embedding. We offer another proof of this result using a distance estimate via hyperbolic 3-manifolds.

We develop the theory of diagrammatic Temperley-Lieb categories in order to construct examples of spherical fusion categories, which we then use to construct Turaev-Viro skein modules for n-holed disks. This is a thesis submitted for the degree of Bachelor of Science with Honours at the Australian National University.

Current-voltage (I-V) characteristics of Tl2Ba2CaCu2O8 thin films in zero magnetic field are measured and analyzed with the conventional Kosterlitz-Thouless-Berezinskii (KTB) approach, dynamic scaling approach and finite-size scaling approach, respectively. It is found from these results that the I-V relation is determined by the vortex-unbinding mechanism with the KTB dynamic critical exponent z = 2. On the other hand, the evidence of finite-size effect is also found, which blurs the feature of a phase transition.

The cohomology jump loci of a space X are of two basic types: the characteristic varieties, defined in terms of homology with coefficients in rank one local systems, and the resonance varieties, constructed from information encoded in either the cohomology ring, or an algebraic model for X. We will explore in this talk the geometry of these varieties and the delicate interplay between them in the context of compact, orientable 3-manifolds. In the  process, we will arrive at a fairly precise geometric description of the resonance varieties R^i_k(A) of a 3-dimensional Poincaré duality algebra A.

Current-voltage (I−V) characteristics of Tl2Ba2CaCu2O8 thin films in zero magnetic field are measured and analyzed with the conventional Kosterlitz-Thouless-Berezinskii (KTB) approach, dynamic scaling approach and finite-size scaling approach, respectively. It is found from these results that the I−V relation is determined by the vortex-unbinding mechanism with the KTB dynamic critical exponent z = 2. On the other hand, the evidence of finite-size effect is also found, which blurs the feature of a phase transition.

Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe.