In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, and also to submanifolds in manifolds, and suitable subsets of algebraic varieties.
The dual concept is relative dimension.
Read more about Codimension: Definition, Additivity of Codimension and Dimension Counting, Dual Interpretation, In Geometric Topology
Other articles related to "codimension, codimensions":
Classification Of Manifolds - Maps Between Manifolds - Low Codimension
... to the classification of manifolds, in high codimension (meaning more than 2), embeddings are classified by surgery, while in low codimension or in relative dimension, they are ... In codimension greater than 2, embeddings are classified by surgery theory ... In codimension 2, particularly embeddings of 1-dimensional manifolds in 3-dimensional ones, one has knot theory ...
... to the classification of manifolds, in high codimension (meaning more than 2), embeddings are classified by surgery, while in low codimension or in relative dimension, they are ... In codimension greater than 2, embeddings are classified by surgery theory ... In codimension 2, particularly embeddings of 1-dimensional manifolds in 3-dimensional ones, one has knot theory ...
Classification Of Manifolds - Dimension 5 and More: Surgery
... dimension 5 is the cut-off because the middle dimension has codimension more than 2 when the codimension is 2, one encounters knot theory, but when the ...
... dimension 5 is the cut-off because the middle dimension has codimension more than 2 when the codimension is 2, one encounters knot theory, but when the ...
Bifurcation Theory - Codimension of A Bifurcation
... The codimension of a bifurcation is the number of parameters which must be varied for the bifurcation to occur ... This corresponds to the codimension of the parameter set for which the bifurcation occurs within the full space of parameters ... are the only generic local bifurcations which are really codimension-one (the others all having higher codimension) ...
... The codimension of a bifurcation is the number of parameters which must be varied for the bifurcation to occur ... This corresponds to the codimension of the parameter set for which the bifurcation occurs within the full space of parameters ... are the only generic local bifurcations which are really codimension-one (the others all having higher codimension) ...
Codimension - In Geometric Topology
... Codimension also has some clear meaning in geometric topology on a manifold, codimension 1 is the dimension of topological disconnection by a. 5 and above, can alternatively be said to start in codimension 3, because higher codimensions avoid the phenomenon of knots ... up to the middle dimension, once one is in dimension 5, the middle dimension has codimension greater than 2, and hence one avoids knots ...
... Codimension also has some clear meaning in geometric topology on a manifold, codimension 1 is the dimension of topological disconnection by a. 5 and above, can alternatively be said to start in codimension 3, because higher codimensions avoid the phenomenon of knots ... up to the middle dimension, once one is in dimension 5, the middle dimension has codimension greater than 2, and hence one avoids knots ...
Polyhedral Space - Curvature
... Nonnegative curvature on singularities of codimension 2 implies nonnegative curvature overall ... Then on the edges of this octant (singularities of codimension 2) the curvature is nonpositive (because of branching geodesics), yet it is not the case at the origin (singularity of ...
... Nonnegative curvature on singularities of codimension 2 implies nonnegative curvature overall ... Then on the edges of this octant (singularities of codimension 2) the curvature is nonpositive (because of branching geodesics), yet it is not the case at the origin (singularity of ...
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