Topology

Black Matter, Lightning and Cuts. Structural Film as a Minoritarian Practice

by Matej T. Vatovec

AFRICANIDADE, ESPAÇO E TRADIÇÃO A TOPOLOGIA DO IMAGINÁRIO ESPACIAL TRADICIONAL AFRICANO NA FALA "GRIOT" SOBRE SUNDJATA KEITA DO MALI

by Maurício Waldman

Il n’y a pas de rapport sexuel: The Irresolvability of the Gadamer-Habermas Debate

by William J. Urban

class paper written Good Friday, April 6, 2012

Topology-dependent description of grain

by Hao Wang

published in EPL, 96 (2011) 38003

A growth equation for individual grains is suggested by considering the interactions
of the nearest-neighbor... more A growth equation for individual grains is suggested by considering the interactions
of the nearest-neighbor grains, which indicates that the average grain growth rate of a given
topological class depends on the difference between the number of faces and the average number
of faces of the nearest neighbors. For the convenience of its application, a practical equation is
also proposed. They have been verified by the data of Beta-titanium grains, dry 3D foams, Monte
Carlo Potts model simulation, vertex model simulation, and surface evolver simulation.

Modeling Interdependent Network Security from a Quantitative and Qualitative Perspective

by Alan Nochenson

Co-authored w/ C. F. Larry Heimann

This paper looks at network security from a game-theoretic point of view. Through the formulation and examination of... more This paper looks at network security from a game-theoretic point of view. Through the formulation and examination of increasingly complex scenarios, we formulate a model for utility-based security decisions. We look at the decision for one person to connect to the internet, to buy security software for herself, and to buy security software in the context of two or more people. By modeling security as a public good, we examine externalities that players impose upon each other. We then examine Olson’s theory of groups in a network security context to evaluate the effect of network size on optimal decision-making. Network topologies are also discussed briefly to investigate the limitations of the models proposed here. We conclude that these models work well for small to medium-sized networks with fairly randomly-distributed topologies.

Introduction à la topologie du temps

by Raphaël Millière

communication à l'Atmoc du 17 février 2012

Le champ d’investigation ouvert par l’étude rigoureuse de la topologie du temps, qui demeure relativement marginal,... more Le champ d’investigation ouvert par l’étude rigoureuse de la topologie du temps, qui demeure relativement marginal, est un bon exemple de l’intérêt du formalisme pour faire progresser nos intuitions confuses et réviser nos concepts inadéquats concernant le temps. On sait quelle fut toujours la difficulté des philosophes, depuis Aristote, à déterminer la nature exacte du temps sans sombrer dans le paradoxe et la métaphore. Réfléchir sur la topologie du temps permet précisément de s’interroger en détail sur les propriétés de tel ou tel système temporel, sans s’engager en faveur du platonisme (les « items » temporels, e.g. les instants, existent indépendamment des événements) ou du réductionnisme (ces items temporels sont réductibles à des collections d’événements). Il s’agit donc, au sens large, d’un exercice d’ontologie formelle, mais l’aspect empirique de l’enquête telle qu’elle est présentée par William Newton-Smith (1980) le situe également à la frontière de l’ontologie traditionnelle et de la physique théorique.

http://www.atmoc.fr/publications

Ordering the Reidemeister moves of a classical knot

by Alexander Coward

Alg. Geom. Top. 6 (2006) 659-671

We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are... more We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type.

Algorithmically detecting the bridge number of hyperbolic knots

by Alexander Coward

We show that, up to ambient isotopy, the exterior of a hyperbolic knot in the 3-sphere admits finitely many bridge... more We show that, up to ambient isotopy, the exterior of a hyperbolic knot in the 3-sphere admits finitely many bridge punctured 2-spheres of given Euler characteristic and that there is an algorithm to find all of these surfaces. This yields an algorithm to detect bridge number for hyperbolic knots.

Unknotting genus one knots

by Alexander Coward

Comment. Math. Helv. 86 (2011) 383-399

For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is... more For any knot with genus one and unknotting number one, other than the figure-eight knot, we prove that there is exactly one way to unknot it by means of a crossing change. In the case of the figure-eight knot, we prove that there are precisely two unknotting crossing changes. The proof uses sutured manifold theory and an analysis of the arc complex of the once-punctured torus.

An upper bound on Reidemeister moves

by Alexander Coward

Submitted

We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the... more We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links.

Network topologies and virtual place

by Paul Adams

The use of terms such as "cyberspace," "electronic frontier," and "information... more The use of terms such as "cyberspace," "electronic frontier," and "information superhighway" implies a project for geographers: the attempt to incorporate such innovative views of place within an ontological framework sensitive to geographical concerns. Combinatorial theory and structuration theory provide a basis for this incorporation. Just as places are dialectically related to social processes, so too are communication media. Similar factors related to the patterning of communication flows pertain in both cases. In particular, geographers can identify similar patterns of nodes (communicators) and links (communication paths) in places and in communication media. These patterns, or topologies, provide a set of opportunities and constraints for social interaction. They can be compared quantitatively through the use of combinatorial theory.

Inroduction to Cobordism Categories and TQFTs

by Shay Logan

This paper is a hand-wavy and overly general introduction to cobordism theory and TQFTs

Locally precompact groups: (Local) realcompactness and connectedness

by Gabor Lukacs

Co-authored with W.W. Comfort. Published in Journal of Lie Theory 20 (2010), no. 2, 347-374.

A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and... more A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties:
Dieudonn\'e completeness; local realcompactness; realcompactness; hereditary realcompactness; connectedness; local connectedness; zero-dimensionality. They also prove that an abelian locally precompact group occurs as the quasi-component of a topological group if and only if it is precompactly generated, that is, it is generated algebraically by a precompact subset.

Éléments D'Une Topologie Classique: Les Comédies De Molière= Elements for a Topology of Classicism: Molière's Comedies

by Llewellyn BROWN

Littérature n° 147, septembre 2007, p. 69-83.

Synthesis of Dancing Motions Based on a Compact Topological Representation of Dance Styles

by Luiz Naveda

Lobato, J. a., Naveda, L. A. B., Gouyon, F., Leman, M., and Reis, J. a. P. (2010). Synthesis of Dancing Motions Based on a Compact Topological Representation of Dance Styles. In IROS2010, Taipei.

Synthesis of Variable Dancing Styles Based on A Compact Spatiotemporal Representation of Dance

by Luiz Naveda

Oliveira, J. a. L., Naveda, L., Gouyon, F., Leman, M., and Reis, J. a. P. (2010). Synthesis of variable dancing styles based on a compact spatiotemporal representation of dance. In IROS2010, Taipei.

The spatiotemporal representation of dance and music gestures using Topological Gesture Analysis (TGA)

by Luiz Naveda

Naveda, L. and Leman, M. (2010). The spatiotemporal representation of dance and music gestures using Topological Gesture Analysis (TGA). Music Perception, 28(1):93–111.

Spatiotemporal gestures in music and dance have
been approached using both qualitative and quantitativemore Spatiotemporal gestures in music and dance have
been approached using both qualitative and quantitative
research methods. Applying quantitative methods
has offered new perspectives but imposed several constraints
such as artificial metric systems, weak links with
qualitative information, and incomplete accounts of
variability. In this study, we tackle these problems using
concepts from topology to analyze gestural relationships
in space. The Topological Gesture Analysis (TGA) relies
on the projection of musical cues onto gesture trajectories,
which generates point clouds in a three-dimensional
space. Point clouds can be interpreted as topologies
equipped with musical qualities, which gives us an idea
about the relationships between gesture, space, and
music. Using this method, we investigate the relationships
between musical meter, dance style, and expertise
in two popular dances (samba and Charleston). The
results show how musical meter is encoded in the dancer’s
space and how relevant information about styles
and expertise can be revealed by means of simple topological
relationships.

“No Outside of Psychoanalysis”: Towards a Grammatological Concept of the Unconscious

by Henrik S Wilberg

Mosaic - A Journal for the Interdisciplinary Study of Literature, Volume 44 - No. 3 (September 2011)

This essay proposes a new reading of the relation between deconstruction and psychoanalysis. Rejecting the terms of... more This essay proposes a new reading of the relation between deconstruction and psychoanalysis. Rejecting the terms of the previous confrontations between the positions of Derrida and Lacan, the essay seeks to show how the scope of what Derrida proposed under the title of grammatology can be extended beyond the limits of the “Freudian impression” and provide a key to understanding the complex topological notions Lacan developed in his later years.

The Classification of Curves

by Jonathan Gleason

The paper I wrote for the Winter 2010 University of Chicago Mathematics DRP.

We introduce the theory of simplicial complexes and use it to prove the triangulability of $1$-manifolds. We then use... more We introduce the theory of simplicial complexes and use it to prove the triangulability of $1$-manifolds. We then use this result to classify all $1$-manifolds.