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- Free_loop abstract "In the mathematical field of topology, a free loop is a variant of the mathematical notion of a loop. Whereas a loop has a distinguished point on it, called a basepoint, a free loop lacks such a distinguished point. Formally, let be a topological space. Then a free loop in is an equivalence class of continuous functions from the circle to . Two loops are equivalent if they differ by a reparameterization of the circle. That is, if there exists a homeomorphism such that .Thus, a free loop, as opposed to a based loop used in the definition of the fundamental group, is a map from the circle to the space without the basepoint-preserving restriction. Free homotopy classes of free loops correspond to conjugacy classes in the fundamental group.In the last years, interest in the space of all free loops has grown with the advent of string topology, i.e. the study of new algebraic structures on the homology of the free loop space.".
- Free_loop wikiPageExternalLink 0503625.
- Free_loop wikiPageID "18742821".
- Free_loop wikiPageRevisionID "577595235".
- Free_loop hasPhotoCollection Free_loop.
- Free_loop subject Category:Knot_theory.
- Free_loop subject Category:Topology.
- Free_loop comment "In the mathematical field of topology, a free loop is a variant of the mathematical notion of a loop. Whereas a loop has a distinguished point on it, called a basepoint, a free loop lacks such a distinguished point. Formally, let be a topological space. Then a free loop in is an equivalence class of continuous functions from the circle to . Two loops are equivalent if they differ by a reparameterization of the circle.".
- Free_loop label "Free loop".
- Free_loop label "Vrije lus".
- Free_loop label "عقدة حرة".
- Free_loop sameAs Vrije_lus.
- Free_loop sameAs m.04gm_ss.
- Free_loop sameAs Q2015432.
- Free_loop sameAs Q2015432.
- Free_loop wasDerivedFrom Free_loop?oldid=577595235.
- Free_loop isPrimaryTopicOf Free_loop.