Fundamental group

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Revision 1243

8/13/2026, 9:40:57 AM · Ancient Tree

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domain~~Topology~~Algebraic topology

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1## Intuitive definition

The fundamental group of a [[Topological space|topological space]] $X$ at a base point $x_{0}$ is the [[Group|group]] of homotopy classes of [[loop|loops]] of $X$ based at $x_{0}$, where the group operation is induced by concatenation of loops. It is denoted by

2$$\pi_{1}(X,x_{0}).$$

3To be completed.

5## Formal definition

7To be completed with LaTeX.

9## Examples

11- Example linked to [[polynomial]].

Revision 442

7/16/2026, 10:59:30 AM · Ancient Tree

Concept created

## Intuitive definition

To be completed.

## Formal definition

To be completed with LaTeX.

## Examples

- Example linked to [[polynomial]].