Linked from

The 29 pages that link to Fundamental group, each with the reason it gives.

• TopologyRelated: It detects certain holes by recording how loops can or cannot contract.

• Fundamental theorem of algebraRelated: A topological proof studies how polynomial values wind around zero along large circles.

• Topological spaceRelated: It extracts algebraic information about loops from a space's topology.

• Configuration spaceRelated: It detects whether point motions can be continuously undone without collisions.

• SubgroupRelated: Its subgroups encode covering spaces of a connected, suitably well-behaved space.

• Simply connected spaceRelated: A space is simply connected exactly when this group is trivial.

• HomeomorphismRelated: Homeomorphic spaces have isomorphic fundamental groups, a useful obstruction to equivalence.

• FunctorRelated: The fundamental group construction maps continuous maps to group homomorphisms.

• Poincaré conjectureRelated: Poincaré’s formulation connects trivial loop structure with the topology of a three-manifold.

• TorusRelated: Its fundamental group is the free abelian group on two generators.

• Free groupRelated: The fundamental group of a graph is free, with rank determined by its independent cycles.

• Branch pointRelated: Loops around deleted branch points determine the continuation transformations.

• Equivalence classRelated: Its elements are equivalence classes of loops under homotopy.

• Möbius stripRelated: The strip has the same fundamental group as a circle, revealing its loop structure.

• SU(2)Related: SU(2) is simply connected, whereas SO(3) has a nontrivial fundamental group.

• Systolic geometryRelated: It records whether loops represent nontrivial classes relevant to systolic lengths.

• Mostow rigidity theoremRelated: An isomorphism between these groups is the theorem’s topological input.

• Grothendieck–Katz p-curvature conjectureRelated: Analytic continuation around loops supplies the group underlying monodromy.

• Myers's theoremRelated: Myers's theorem also constrains the manifold's loop classes to form a finite group.