Examples of 'fundamental group' in a sentence
Meaning of "fundamental group"
In mathematics, the fundamental group is a concept in algebraic topology that represents the collection of all possible loops in a topological space. It is a fundamental tool for studying the properties of spaces and their deformations. The fundamental group serves to classify spaces and distinguish between homotopy-equivalent spaces. It provides important information about the connectivity, shape, and fundamental structure of a given space
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- For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.
How to use "fundamental group" in a sentence
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fundamental group
Expansive flows and the fundamental group.
Fundamental group and dependence on the base point.
In the case it is also called the fundamental group.
Its fundamental group is trivial.
It is true if and only if the fundamental group is abelian.
The fundamental group is the first and simplest homotopy group.
Homotopy and fundamental group.
A fundamental group of a compact complete flat affine manifold is called an affine crystallographic group.
A surface with a trivial fundamental group is said to be simply connected.
There are several ways to define the orbifold fundamental group.
We affirm that the fundamental group unit of society is the family.
Free homotopy classes of free loops correspond to conjugacy classes in the fundamental group.
Has a nontrivial fundamental group.
The fundamental group has a normal central infinite cyclic subgroup of finite index.
The family is the natural and fundamental group unit of society.
See also
The orbifold fundamental group is the group formed by homotopy classes of orbifold loops.
The family as the natural and fundamental group unit of society.
The fundamental group of a connected Lie group is always commutative.
Analogous results for the tame fundamental group are discussed as well.
The fundamental group of the presentation complex is the group G itself.
These results applied to the algebraic fundamental group and to the Picard group.
The fundamental group of a ( finite ) simplicial complex does have a finite presentation.
The real projective plane has a fundamental group that is a cyclic group with two elements.
Then, homeomorphic spaces have isomorphic fundamental group.
Determining whether the fundamental group of a finite simplicial complex is trivial.
So these three-manifolds are completely determined by their fundamental group.
They are a more fundamental group than the Sunnis.
More generally, any contractible space has a trivial fundamental group.
Animations to introduce fundamental group by Nicolas Delanoue.
The corresponding manifolds are exactly the closed 3-manifolds with finite fundamental group.
A sphere 's fundamental group is therefore trivial.
Is every topological group the topological fundamental group of an space?
Therefore, the fundamental group of the sphere is trivial.
In other words, the monodromy is a two dimensional linear representation of the fundamental group.
For example, elements of the fundamental group are represented by loops.
The fundamental group is a topological invariant, homeomorphic topological spaces have the same fundamental group.
A path-connected space with a trivial fundamental group is said to be simply connected.
The fundamental group of an H-space is abelian.
The automorphism group of a point x0 in X is just the fundamental group based at x0.
This way, the fundamental group detects the hole.
The Covenant protects the family as " the natural and fundamental group unit of society.
More generally, the fundamental group of any graph is a free group.
According to the Constitution, the family is the natural and fundamental group unit of society.
Conversely, the fundamental group of any closed manifold is finitely presented.
There is a complete classification of three-dimensional lens spaces, by fundamental group and Reidemeister torsion.
In algebraic topology, the fundamental groupoid of a topological space is a generalization of the fundamental group.
For compact Lie groups, there are two basic approaches to computing the fundamental group.
A path-connected space whose fundamental group is trivial is called simply connected.
The sphere is simply connected, while the real projective plane has fundamental group Z2.
Poincaré introduced the fundamental group to distinguish different categories of two-dimensional surfaces.
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