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Topic: Isotopy

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	Bakhtin's "voice," Greimas’ "isotopy" (Site not responding. Last check: 2007-10-21)
		The basis of the idea is that music may be understood in a manner similar to prose discourse.
		These voices may be either "monologic" or "dialogic" and, through their interaction, prose discourse becomes a complex, "polyphonic" dialogue of both types of voice.
		In addition, I suggest that "voice" in both music and literature, may be understood and analyzed in terms of Greimas' "discursive isotopy": a redundancy, or iterativity, of semantic content throughout discourse, producing within the utterance a semantic coherence.
	www.tau.ac.il /arts/musicology/INTERP/liddle.htm (301 words)

	Isotopy
		Isotopy was originally said to consist in the permanence of contextual features ("classemes"), whose variations, instead of destroying the unity of the "text", serve to confirm it.
		Thus, in the toast isotopy, the term "poupe" (that is, literally, "stern") from the sailing isotopy, retains its abstract features [+extremity] and [+posteriority], becoming a metaphor for the end of the table.
		Indeed, as soon as we realise that the story in question is a joke, we expect the non-expected to occur – in a particular case, we may, in Greimasean terms, expect a rupture of isotopy, that is, a non-recurrence of the same units, an allotopy.
	www.arthist.lu.se /kultsem/encyclo/isotopy.html (2340 words)

	Latin square - Wikipedia, the free encyclopedia
		If we permute the rows, permute the columns, and permute the names of the symbols of a Latin square, we obtain a new Latin square said to be isotopic to the first.
		Isotopism is an equivalence relation, so the set of all Latin squares is divided into subsets, called isotopy classes, such that two squares in the same class are isotopic and two squares in different classes are not isotopic.
		Another type of operation is easiest to explain using the orthogonal array representation of the Latin square.
	en.wikipedia.org /wiki/Latin_square (790 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		An isotopy of a planar graph G is a continuous family of embeddings of G. We will describe a method for constructing isotopies of planar graphs with fixed boundary, initially motivated by applications to deformations and morphing, and relying on a theorem by Tutte to build embeddings of planar graphs.
		Considering both embeddings of G (with the same boundary) between which an isotopy has to be built, we have to view them as equilibrium states of two such physical systems, and to interpolate linearly the barycentric coefficients.
		Finally, we study the same isotopy problem in three dimensions, and show that things are more complicated: there exist two embeddings of a 3-dimensional simplicial complex with the same boundary which are combinatorially equivalent but for which there exists no isotopy from one to the other.
	www.loria.fr /~lazard/ARC-Visi3D/Abstracts/abstract_eric-colin_0901.html (255 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		There are lots of non-isotopic framed embeddings of the circle in R^3, where by framed embedding I mean an embedding together with a trivialization of the normal bundle, and isotopy means the hopefully obvious sort of smooth 1-parameter family of such framed embeddings.
		In fact, isotopy classes of framed embeddings of the circle in R^3 should be the same as isotopy classes of "framed oriented knots".) Now such a framed embedding in R^3 automatically gives a framed embedding in R^4 --- just stick on another coordinate.
		Now similarly we get maps F: {isotopy classes of framed embeddings of a circle in R^m} -> {isotopy classes of framed embeddings of a circle in R^{m+1}} for all m, but I think these are 1-1 and onto for m >= 4.
	www.math.niu.edu /~rusin/papers/known-math/95/isotopy (418 words)

	[No title]
		The isotopy thus extends by the identity isotopy on $\Cn0$ to an ambient isotopy in $M$ which carries $P$ to a plane $P\p$ which is in $n_0$-standard position with respect to $C$.
		There is an ambient isotopy of $P$ in $M$ supported in $B_3$ which consists of a boundary slide of $\be$ past $\be\p$, followed by a boundary slide of $\de$ past $\de\p$, followed by a disk push which replaces $Z$, $Z_1$, and $Z_2$ by a patch $Y$ in $X_{n+2}$ of order at least two.
		The only other possible effects of this isotopy on $\Gamma$ are to collapse other such falling stars with centers in $X$ in a similar fashion and to amalgamate vertices in $X_{n+2}$ which are adjacent to vertices in $X$, thereby reducing the orders of these vertices, but not reducing them to one.
	www.math.okstate.edu /preprint/1996/temp.4b (14252 words)

	Comb. Structures Lecture Notes 1
		Isotopy is an equivalence relation on the set of Latin squares of a given order
		The resulting square is of course isotopic to the original square and is a convenient representative of the isotopy class of this square.
		There is only one isotopy class of order 2 squares, and only one for order 3 squares.
	www-math.cudenver.edu /~wcherowi/courses/m6406/csln1.html (1592 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		A unifying theme in the paper is the analysis and application of isotopy stable dynamics, i.e.
		These coordinates record the isotopy, homotopy, or homology class of the corresponding orbit in the suspension flow.
		The isotopy stable coordinates are then characterized, and it is shown that there is a map in each isotopy class that has just these periodic orbits and no others.
	www.math.sunysb.edu /dynamics/surveys/top.html (247 words)

	Approches to the Lifeworld core of pictorial rhetoric (1)
		But the isotopy, as Greimas (1966: 96; 1970: 10, 188; 1972: 8) affirms and Groupe µ (1977:30ff) repeats, is involved with redundancy and coherence; and as a formal operation, it merely yields an unordered set of lexemes or, more exactly, semantic features.
		Instead of the notion of isotopy, we thus need a concept such as the scheme of interpretation, which accounts for the way the world is expected to be organised, permitting a comparison with the way it actually turns out to be.
		But there is no rupture of isotopy in homogeneous transformations: they rather constitute an infraction of the historical norm stipulating the way in which objects are to be rendered in pictures.
	www.arthist.lu.se /kultsem/sonesson/RhetoricalApproach1.html (4815 words)

	A Little Glossary of Semantics
		interlaced: this is said of lexicalized isotopies whose sememes alternate in sequences or chains that are at a lower level than the dimension of the period.
		poly-isotopy: in the limited sense it is the property of a linguistic chain that includes several generic isotopies whose isotopizing semes are in a relation of incompatibility; in the larger sense, the property of a chain that includes more than one isotopy.
		semantic isotopy: effect of a recurrence of one and the same seme.
	www.revue-texto.net /Reperes/Glossaires/Glossaire_en.html (1803 words)

	Homotopy (Site not responding. Last check: 2007-10-21)
		In case the two given continuous functions f and g from the topological space X to the topological space Y are homeomorphisms, one can ask whether they can be connected 'through homeomorphisms'.
		This gives rise to the concept of isotopy, which is a homotopy H in the notation used before, such that for each fixed t, H(x,t) gives a homeomorphism.
		In geometric topology - for example in knot theory - the idea of isotopy is used to construct equivalence relations.
	www.worldhistory.com /wiki/H/Homotopy.htm (951 words)

	[No title]
		Munkres, Differentiable isotopies on the 2-sphere, Mich. Math.
		As the lengths of these papers indicate, the proofs, while sneaky, are not apparently not insanely complicated, though I didn't read it.
		My main semi-interesting comment in this whole affair is that John Baez's second question concerned isotopy of diffeomorphisms of a ball B^n, but this is equivalent to considering the above twoer for S^n.
	www.math.niu.edu /~rusin/known-math/93_back/smooth_sn (917 words)

	Knot Theory
		Isotopy: two knots or links are considered equivalent when one is obtained from the other by continuous deformation where at each point in time we have a homeomorphic image of S
		Kauffman has his knot crystals (union of the set of arcs, and the fundamental group of the complement of the knot, with two injections from the first into the second, and a right action of the second on the first), invariant for regular isotopy.
		Joyce has his quandle, a quotient of the knot crystal, that is invariant for isotopy.
	www.win.tue.nl /~amc/ow/knots (1422 words)

	Glossary (Site not responding. Last check: 2007-10-21)
		The deformation of the teapot to a torus is an isotopy, but the deformation to a point is not.
		A surface that locally has the smallest area given a particular topological shape for it, and possibly, constrained by a fixed boundary (soap-films) or prescribed behavior at infinity.
		A particular way of guiding an isotopy of an embedded surface to one which minimizes a function that measures its shape.
	www.geom.uiuc.edu /docs/research/ieee94/node21.html (341 words)

	Virtual Knots
		In terms of knot diagrams, ambient isotopies translate to sequences of plane isotopies and Reidemeister moves.
		A plane isotopy allows us to move a curve around in the plane, stretching or bending it however we want so long as we don't intersect it with another curve or move it out of the plane.
		There is a theorem which says that two knot diagrams arising from ambient isotopic knots are related by a series of plane isotopies and Reidemeister moves, and conversely plane isotopies and Reidemeister moves can be "lifted" to obtain ambient isotopies in knots.
	www.math.lsu.edu /~nelson/vknots.html (2679 words)

	Holomorphic K -theory, A linearization of the topology of the stable mapping class group (Site not responding. Last check: 2007-10-21)
		Holomorphic K -theory, A linearization of the topology of the stable mapping class group
		In this talk I will describe how to adapt the calculus of isotopy functors to functors from a certain 2 - category of open sets in surfaces.
		is a linear isotopy functor, and that the Madsen - Tillmann map
	www.maths.abdn.ac.uk /~stc2001/abstracts/RCohen/RCohen.html (268 words)

	Combinatorial Data (Site not responding. Last check: 2007-10-21)
		The two most common equivalence classes defined for Latin squares are isotopy classes and main classes.
		Two squares are in the same isotopy class if one can be obtained from the other by permuting rows, columns and symbols.
		To be in the same main class, one is in addition permitted to permute the three roles "row", "column" and "symbol" (for example, symbol s in row r and column c might become symbol r in row c and column s).
	cs.anu.edu.au /~bdm/data/latin.html (234 words)

	THE ISOTOPY CLASSIFICATION OF AFFINE QUARTIC CURVES (Site not responding. Last check: 2007-10-21)
		In this paper we obtain the isotopy classification of affine quartic curves, which contains 647 classes, and the topological classification of pairs (
		We also present the isotopy classification of real projective quartic curves, which contains 66 classes.
		We prove that each of these classifications is equivalent to the classification of all real (affine or projective) quartic curves having only singular points, if any, of types
	math.la.asu.edu /~rmmc/rmj/vol32-1/KOR (84 words)

	[No title]
		Recall: $\LSymp(M,\omega)$ is not simple (because it consists of closed 1-forms...) Hamiltonian vector fields give a notion of {\em Hamiltonian isotopy} in $\Symp(M,\omega)$ (namely, an isotopy $(\phi_t)$ such that $X_t=\phi^*_t(\partial \phi_t/\partial t)$ is Hamiltonian).
		Isotopy thm: Suppose $N_t \subset M$ is a smooth family of symplectic submanifolds.
		Pf: The isotopy gives a $t$-dependent exact 1-form, and hence a $t$-dependent function.
	www.math.uchicago.edu /~msmukler/oct05 (1051 words)

	Citations: Classical Topology and Combinatorial Group Theory - Stillwell (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		We will therefore, for reasons of convenience, refer to an orientation preserving homeomorphism of R 2 as an isotopy of R 2.
		An isotopy is a homotopy h t for which every h t (x) is a homeomorphism.
		Homotopy is an essential tool for classifying manifolds of low dimensions, while isotopy is instrumental in knot theory [25] Fig.
	citeseer.ist.psu.edu /context/178779/0 (3023 words)

	List of Publications (Site not responding. Last check: 2007-10-21)
		Allen E. Hatcher, Concordance and isotopy of smooth embeddings in low codimensions.
		Allen Hatcher and Frank Quinn, Bordism invariants of intersections of submanifolds.
		Allen Hatcher and Terry Lawson, Stability theorems for "concordance implies isotopy" and "h-cobordism implies diffeomorphism".
	www.math.cornell.edu /~hatcher/Papers/publist.html (342 words)

	Topology HW #2 (Site not responding. Last check: 2007-10-21)
		This will sometimes be referred to as "planar isotopy" and its equivalent to the R0 move.)
		Classify all of the link diagrams with two crossings up to isotopy.
		Say as much as you can about the classification of link diagrams with two crossings up to regular isotopy.
	www.math.ou.edu /~amiller/4853-00/hw/hw2.htm (169 words)

	Analysis and Geometry Seminar (Site not responding. Last check: 2007-10-21)
		The symplectic isotopy problem asks for the classification
		up to isotopy of symplectic submanifolds in positive manifolds, such
		Conjecturally there is an algebraic curve in each isotopy
	www.math.rutgers.edu /~feehan/seminar/siebert.html (78 words)

	Physically-Based Stochastic Simplification of Mathematical Knots (Site not responding. Last check: 2007-10-21)
		This configuration is believed to be characteristic for its knot type.
		We propose a physically-based model to implicitly guard against isotopy violation during such evolution and suggest that a robust stochastic optimization procedure, simulated annealing, be used for the purpose of identifying the globally optimal solution.
		Because neither of these techniques depends on the properties of the energy function being optimized, our method is of general applicability, even though we applied it to a specific potential here.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tg/&toc=comp/trans/tg/1997/03/v3toc.xml&DOI=10.1109/2945.620492 (588 words)

	M-curves
		In 1938 I.G. Petrovsky [4] gave curves with the maximum number of components
		D. Hilbert [3] included the problem of isotopy classification of
		In order to describe the isotopy class of a curve we will use the coding scheme devised by Viro[6].
	pages.prodigy.net /danesmith/mcurve/mcurve.html (889 words)

	Etta Falconer - Mathematician of the African Diaspora
		In 2002, Dr. Falconer ret red as Callaway Professor of Mathematics and Associate Provost for Science Programs and Policy, Spelman College
		After a few years of teaching at the junior college/college level, she entered Emory University in Atlanta.
		In 1969 she became the 10th African American woman to earn a Ph.D. in Mathematics (from Emory University) with an Algebra dissertation entitled: "Quasi group Identities Invariant under Isotopy."
	www.math.buffalo.edu /mad/PEEPS/falconner_ettaz.html (1219 words)

	Definition of isotopy - Merriam-Webster Online Dictionary
		isotopy is one of more than 1,000,000 entries available at Merriam-WebsterUnabridged.com.
		For More Information on "isotopy" go to Britannica.com
		Get the Top 10 Search Results for "isotopy"
	www.m-w.com /dictionary/isotopy (82 words)

	Physics Help and Math Help - Physics Forums - View Single Post - Isotopy in Topology
		Physics Help and Math Help - Physics Forums - View Single Post - Isotopy in Topology
		I am not an expert but my impression is that linking is a phenomenon related to an enclosing space.
		Also a space can be linked upon itself.
	www.physicsforums.com /showpost.php?p=281965&postcount=2 (81 words)

	Geometric Knot Spaces And Polygonal Isotopy (ResearchIndex) (Site not responding. Last check: 2007-10-21)
		The space of n-sided polygons embedded in three-space consists of a smooth manifold in which points correspond to piecewise linear or "geometric " knots, while paths correspond to isotopies which preserve the geometric structure of these knots.
		@misc{ calvo-geometric, author = "Jorge Alberto Calvo", title = "Geometric Knot Spaces And Polygonal Isotopy", url = "citeseer.ist.psu.edu/106707.html" }
		Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
	citeseer.ist.psu.edu /106707.html (400 words)

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