Examples of 'homotopy' in a sentence
Meaning of "homotopy"
Homotopy (noun) - a continuous deformation between two mathematical objects, such as curves or functions, while keeping some property invariant
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- A continuous deformation of one continuous function or map to another.
- The relationship between two continuous functions where homotopy from one to the other is evident.
- Ellipsis of homotopy theory. (the systematic study of homotopies and their equivalence classes).
- A theory associating a system of groups with each topological space.
How to use "homotopy" in a sentence
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homotopy
Typical definition of homotopy and homotope are as follows.
Homotopy colimits in the category of small categories.
It is a relative analog of a homotopy equivalence between spaces.
The homotopy pushout rectifies this defect.
The first is that of homotopy contractible complexes.
Then we present shootingalgorithm and homotopy method.
A regular homotopy is thus a homotopy through immersions.
This was the origin of simple homotopy theory.
Rational homotopy theory and differential forms.
Deformation retraction is a particular case of homotopy equivalence.
Homotopy categories are examples of quotient categories.
The history in relation to homotopy groups is interesting.
Homotopy categories and derived categories.
Computational methods for homotopy groups of spheres.
Stable homotopy and generalised homology.
See also
The main computational method is homotopy continuation.
Spaces that are homotopy equivalent to a point are called contractible.
These groups are called the homotopy groups.
These are unique up to homotopy equivalence in a suitable model category.
This can be formulated in terms of homotopy theory.
Therefore the homotopy group is the trivial group.
Reconstructing rational stable motivic homotopy theory.
Equivariant homotopy and cohomology theory.
It is clear how to define a homotopy from to.
The contracting homotopy is constructed using these representations.
It follows that adjoint functors induce homotopy equivalences.
Our contracting homotopy is built using these representations.
Long exact sequence of homotopy groups.
Homotopy theory is deeply related to the stability of topological defects.
Long exact sequence in homotopy for fibrations.
Homotopy groups are such a way of associating groups to topological spaces.
For more discussion see homotopy groups of spheres.
Homotopy groups in algebraic topology.
It is used in calculating the homotopy properties of a simplicial group.
As a direct consequence it follows that if there is a homotopy equivalence.
The development of homotopy in continuous functions.
Homotopy groups of spheres are closely related to cobordism classes of manifolds.
To be the set of homotopy classes of maps.
The homotopy extension property is depicted in the following diagram.
This is called the homotopy hypothesis.
Homotopy groups of the spheres.
This shows that ff is a homotopy equivalence.
Stable homotopy groups of spheres.
He is one of the originators of the field of homotopy type theory.
The goal of rational homotopy theory is to understand this category.
Homotopy and fundamental group.
The fundamental concept of homotopy type theory is the path.
Homotopy and homotopy equivalence.
Her research concerns homotopy theory and homological algebra.
Homotopy types are used to classify the essential features of an object.
