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Topic: Codimension

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	Department of Mathematics - University of Idaho
		One such sub-problem is the classification of non-singular subvarieties of ``low" codimension in projective n-space.
		A basic question in the classification problem is whether for a given set of invariants the corresponding family of varieties is non-empty.
		It appears, however, that non-singular subvarieties of low codimension in projective n-space are exceedingly rare.
	www.uidaho.edu /math/research/algebra.htm (639 words)

	Codimension - Wikipedia, the free encyclopedia
		In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, and more generally to submanifolds in manifolds, and suitable subsets of algebraic varieties.
		The second is a matter of geometry, on the model of parallel lines; it is something that can be discussed for linear problems by methods of linear algebra, and for non-linear problems in projective space, over the complex number field.
		Codimension also has some clear meaning in geometric topology: on a manifold (real) codimension 1 is the dimension of topological disconnection by a submanifold, while codimension 2 is the dimension of ramification and knot theory.
	en.wikipedia.org /wiki/Codimension (455 words)

	Codimension -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-28)
		The fundamental property of codimension lies in its relation to (A junction where one street or road crosses another) intersection: if W
		This statement is more perspicuous than the translation in terms of dimensions, because the (additional info and facts about RHS) RHS is just the sum of the codimensions.
		Codimension also has some clear meaning in (additional info and facts about geometric topology) geometric topology: on a manifold (real) codimension 1 is the dimension of topological disconnection by a submanifold, while codimension 2 is the dimension of (An arrangement of branching parts) ramification and (additional info and facts about knot theory) knot theory.
	www.absoluteastronomy.com /encyclopedia/c/co/codimension.htm (351 words)

	Bristol Centre for Applied Nonlinear Mathematics \| Codimension-two meeting (Site not responding. Last check: 2007-10-28)
		The meeting was part of the activities of the Bristol Centre of Applied Nonlinear Mathematics (Theme B: Bifurcations in nonsmooth dynamical systems).
		The aim of the meeting, which was highly informal, was to have open discussions on how to address the study of higher codimension bifurcations in nonsmooth systems.
		By integrating our experience and know-how, we were able to define a tentative outline of a research programme to be carried out together on the study of such higher-codimension phenomena.
	www.enm.bris.ac.uk /anm/workshop-b/meeting (166 words)

	COG 2.1: cogeometry - definitions
		That means, each point has to be part of one region, or to be part of the boundary of two or more regions.
		Higher codimensions are not possible in 3D, that's why we don't need a name for them.
		A d-segment is a closed subset of X with codimension d.
	www.wias-berlin.de /software/cog/cogdef.html (367 words)

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