Sentence examples for fundamental group from inspiring English sources

'fundamental group' is a correct and usable term in written English.
It is typically used to refer to a group in mathematics that captures the essential properties of a topological space. For example, "The fundamental group of a sphere can be used to determine the number of holes in the surface."

Dictionary

fundamental group

noun

The group whose elements are homotopy classes of images of the closed interval in a specified topological space, such that the endpoints are both mapped to a designated point, and whose operation is concatenation.

Exact(60)

Kong, A digital fundamental group, Comput.

It depends on a representation of the fundamental group.

These delocalized invariants are constructed in terms of a nontrivial conjugacy class of the fundamental group.

Consider a compact locally symmetric space M of rank r, with fundamental group Γ.

Topological spaces and continuous functions, connectedness, compactness, separation axioms, covering spaces, and the fundamental group.

Topics: fundamental group and covering spaces, homology, cohomology, products, basic homotopy theory, and applications.

Fundamental group, covering spaces, Euler characteristic, homology, classification of surfaces, knots.

In a region with no holes, all closed paths are homotopic and the fundamental group consists of a single element.

Let π be the fundamental group of a connected finite graph of groups with finitely generated vertex groups GP.

More generally we consider the co-rank of the fundamental group, also known as the cut number of the manifold.

We will give an outline of the properties of the fundamental group and of representations, if needed.

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