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

... to the classification of manifolds, in high

**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 ...Classification Of Manifolds - Dimension 5 and More: Surgery

... dimension 5 is the cut-off because the middle dimension has

... 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 -

... The

**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**) ...**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 ...

Polyhedral Space - Curvature

... Nonnegative curvature on singularities 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 ...Main Site Subjects

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