Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Homotopy_group> ?p ?o }
- Homotopy_group abstract "In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy groups record information about the basic shape, or holes, of a topological space.To define the n-th homotopy group, the base-point-preserving maps from an n-dimensional sphere (with base point) into a given space (with base point) are collected into equivalence classes, called homotopy classes. Two mappings are homotopic if one can be continuously deformed into the other. These homotopy classes form a group, called the n-th homotopy group, πn(X), of the given space X with base point. Topological spaces with differing homotopy groups are never equivalent (homeomorphic), but the converse is not true.The notion of homotopy of paths was introduced by Camille Jordan.".
- Homotopy_group thumbnail Torus.png?width=300.
- Homotopy_group wikiPageExternalLink hdaweb2.htm.
- Homotopy_group wikiPageExternalLink ATpage.html.
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- Homotopy_group wikiPageWikiLink Abelian_group.
- Homotopy_group wikiPageWikiLink Algebraic_topology.
- Homotopy_group wikiPageWikiLink Allen_Hatcher.
- Homotopy_group wikiPageWikiLink Aspherical_space.
- Homotopy_group wikiPageWikiLink Base_point.
- Homotopy_group wikiPageWikiLink Blakers–Massey_theorem.
- Homotopy_group wikiPageWikiLink CW_complex.
- Homotopy_group wikiPageWikiLink Cambridge_University_Press.
- Homotopy_group wikiPageWikiLink Camille_Jordan.
- Homotopy_group wikiPageWikiLink Category:Homotopy_theory.
- Homotopy_group wikiPageWikiLink Category_(mathematics).
- Homotopy_group wikiPageWikiLink Cohomology.
- Homotopy_group wikiPageWikiLink Complex_number.
- Homotopy_group wikiPageWikiLink Complex_numbers.
- Homotopy_group wikiPageWikiLink Covering_space.
- Homotopy_group wikiPageWikiLink Crossed_module.
- Homotopy_group wikiPageWikiLink Eckmann–Hilton_argument.
- Homotopy_group wikiPageWikiLink Equivalence_class.
- Homotopy_group wikiPageWikiLink Exact_sequence.
- Homotopy_group wikiPageWikiLink Excision_theorem.
- Homotopy_group wikiPageWikiLink Fibration.
- Homotopy_group wikiPageWikiLink Freudenthal_suspension_theorem.
- Homotopy_group wikiPageWikiLink Functor.
- Homotopy_group wikiPageWikiLink Fundamental_group.
- Homotopy_group wikiPageWikiLink Group_(mathematics).
- Homotopy_group wikiPageWikiLink Group_theory.
- Homotopy_group wikiPageWikiLink Groupoid.
- Homotopy_group wikiPageWikiLink Groupoids.
- Homotopy_group wikiPageWikiLink Homeomorphic.
- Homotopy_group wikiPageWikiLink Homeomorphism.
- Homotopy_group wikiPageWikiLink Homology_(mathematics).
- Homotopy_group wikiPageWikiLink Homology_group.
- Homotopy_group wikiPageWikiLink Homomorphism.
- Homotopy_group wikiPageWikiLink Homotopy.
- Homotopy_group wikiPageWikiLink Homotopy_class.
- Homotopy_group wikiPageWikiLink Homotopy_group_with_coefficients.
- Homotopy_group wikiPageWikiLink Homotopy_groups_of_spheres.
- Homotopy_group wikiPageWikiLink Homotopy_lifting_property.
- Homotopy_group wikiPageWikiLink Homotopy_theory.
- Homotopy_group wikiPageWikiLink Hopf_fibration.
- Homotopy_group wikiPageWikiLink Hurewicz_theorem.
- Homotopy_group wikiPageWikiLink Hypercube.
- Homotopy_group wikiPageWikiLink Hypersphere.
- Homotopy_group wikiPageWikiLink Invariant_(mathematics).
- Homotopy_group wikiPageWikiLink Knot_theory.
- Homotopy_group wikiPageWikiLink Loop_(topology).
- Homotopy_group wikiPageWikiLink Mathematical_space.
- Homotopy_group wikiPageWikiLink Mathematics.
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- Homotopy_group wikiPageWikiLink N-connected.
- Homotopy_group wikiPageWikiLink Path_(topology).
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- Homotopy_group wikiPageWikiLink Pointed_space.
- Homotopy_group wikiPageWikiLink Seifert–van_Kampen_theorem.
- Homotopy_group wikiPageWikiLink Serre_fibration.
- Homotopy_group wikiPageWikiLink Serre_spectral_sequence.
- Homotopy_group wikiPageWikiLink Simplicial_set.
- Homotopy_group wikiPageWikiLink Simply_connected_space.
- Homotopy_group wikiPageWikiLink Singular_homology.
- Homotopy_group wikiPageWikiLink Space_(mathematics).
- Homotopy_group wikiPageWikiLink Sphere.
- Homotopy_group wikiPageWikiLink Topological_invariant.
- Homotopy_group wikiPageWikiLink Topological_property.
- Homotopy_group wikiPageWikiLink Topological_space.
- Homotopy_group wikiPageWikiLink Topology.
- Homotopy_group wikiPageWikiLink Torus.
- Homotopy_group wikiPageWikiLink Universal_cover.
- Homotopy_group wikiPageWikiLink Wedge_sum.
- Homotopy_group wikiPageWikiLink File:2sphere_2.png.
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- Homotopy_group wikiPageWikiLink File:Torus.png.
- Homotopy_group wikiPageWikiLinkText "".
- Homotopy_group wikiPageWikiLinkText "Higher homotopy groups".
- Homotopy_group wikiPageWikiLinkText "Homotopy group".
- Homotopy_group wikiPageWikiLinkText "Homotopy group#Long exact sequence of a fibration".
- Homotopy_group wikiPageWikiLinkText "Homotopy group#Relative homotopy groups".
- Homotopy_group wikiPageWikiLinkText "higher homotopy groups".
- Homotopy_group wikiPageWikiLinkText "homotopic".
- Homotopy_group wikiPageWikiLinkText "homotopy group".
- Homotopy_group wikiPageWikiLinkText "long exact sequence of the fibration".
- Homotopy_group wikiPageWikiLinkText "long exact sequence".
- Homotopy_group hasPhotoCollection Homotopy_group.
- Homotopy_group id "p/h047930".
- Homotopy_group title "Homotopy group".
- Homotopy_group wikiPageUsesTemplate Template:Citation.
- Homotopy_group wikiPageUsesTemplate Template:Reflist.
- Homotopy_group wikiPageUsesTemplate Template:Springer.
- Homotopy_group wikiPageUsesTemplate Template:Topology.
- Homotopy_group subject Category:Homotopy_theory.