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Link maps and the geometry of their invariants
Manuscripta Mathematica, 1988 This paper investigates several invariants of link homotopy. A link map consists of two maps \(f_ 1: S^ p\to S^ m\), \(f_ 2: S^ q\to S^ m\) whose images are disjoint; a link homotopy is a one-parameter continuous family of such maps. \(LM^ m_{p,q}\) denotes the set of link homotopy classes.
Ulrich Koschorke
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Rethinking the link between matter and geometry [PDF]
Physical Review D, 2018 In the present manuscript, I examine an intriguing relation at the classical level between general relativity and a theory where matter couples uniquely multiplicatively to geometry in the Lagrangian density. Interestingly, the gravitational constant $G$ is replaced by a novel fundamental constant, whose value is not tied to any classical phenomenon ...
Olivier Minazzoli
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GEOMETRY OF QUANTUM VORTICES AND LINK INVARIANTS
International Journal of Modern Physics B, 1992We report on recent and ongoing research in the context of the geometric approach to quantum vortices and link invariants (via the Marsden-Weinstein theory and Chen’s iterated path integrals).
Penna, Vittorio, Spera, Mauro
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Solvation of Proteins: Linking Thermodynamics to Geometry
Physical Review Letters, 2007We calculate the solvation free energy of proteins in the tube model of Banavar and Maritan [Rev. Mod. Phys. 75, 23 (2003)10.1103/RevModPhys.75.23] using morphological thermodynamics which is based on Hadwiger's theorem of integral geometry. Thereby we extend recent results by Snir and Kamien [Science 307, 1067 (2005)10.1126/science.1106243] to hard ...
Hansen-Goos, H. +3 more
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Geometry Links the Two Spheres
The Arithmetic Teacher, 1986When the educators of today were growing up, little information was available about the brain and its relationship to the acquisition of knowledge. Recent research has hown that the brain functions a two hemispheres, a right side and a left side. Each side influence our learning and emotions and provides the foundation for complementary but different ...
Rosalie Jensen, Deborah C. Spector
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Some links between turtle geometry and analytic geometry
International Journal of Mathematical Education in Science and Technology, 1985The computer language LOGO facilitates the teaching of analytic geometry and calculus from the notion of curvature, through its ‘turtle geometry’ facility [2]. We provide some theoretical basis for finding turtle geometry equivalents of familiar curves in analytic geometry, and vice versa, by some simple methods which apparently have not been noticed ...
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Possible Link Between Isospace and the Geometry of Space-Time
Physical Review Letters, 1964A relation between internal degrees of freedom and event space in quantum field theory is suggested. The event space is considered as a Riemann space in accord with general relativity. The dimension, metric, linear connection, and curvature tensor of the internal space are uniquely determined by the Riemann geometry. (L.B.S.)
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1997
An alternating diagram for a link is, as explained in Chapter 1, one in which the over or under nature of the crossings alternates along every link-component in the diagram; the crossings always go “… over, under, over, under,…” when considered from any starting point. A link is said to be alternating if it possesses such a diagram.
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An alternating diagram for a link is, as explained in Chapter 1, one in which the over or under nature of the crossings alternates along every link-component in the diagram; the crossings always go “… over, under, over, under,…” when considered from any starting point. A link is said to be alternating if it possesses such a diagram.
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On the geometry of homotopy invariants of links
Mathematical Proceedings of the Cambridge Philosophical Society, 1992One of the central problems in higher-dimensional knot theory is the classification of links up to concordance. In 14, Le Dimet constructed a universal model for (disk) link complements, which allowed him to formulate this problem in the framework of surgery theory by applying the Cappell-Shaneson program for studying codimension two embeddings of ...
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