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- Peripheral_subgroup abstract "In algebraic topology, a peripheral subgroup for a space-subspace pair X ⊃ Y is a certain subgroup of the fundamental group of the complementary space, π1(X − Y). Its conjugacy class is an invariant of the pair (X,Y). That is, any homeomorphism (X, Y) → (X′, Y′) induces an isomorphism π1(X − Y) → π1(X′ − Y′) taking peripheral subgroups to peripheral subgroups.A peripheral subgroup consists of loops in X − Y which are peripheral to Y, that is, which stay \"close to\" Y (except when passing to and from the basepoint). When an ordered set of generators for a peripheral subgroup is specified, the subgroup and generators are collectively called a peripheral system for the pair (X, Y).Peripheral systems are used in knot theory as a complete algebraic invariant of knots. There is a systematic way to choose generators for a peripheral subgroup of a knot in 3-space, such that distinct knot types always have algebraically distinct peripheral systems. The generators in this situation are called a longitude and a meridian of the knot complement.".
- Peripheral_subgroup wikiPageExternalLink QuickTrip.pdf.
- Peripheral_subgroup wikiPageID "35865369".
- Peripheral_subgroup wikiPageLength "8389".
- Peripheral_subgroup wikiPageOutDegree "41".
- Peripheral_subgroup wikiPageRevisionID "704093730".
- Peripheral_subgroup wikiPageWikiLink Algebraic_topology.
- Peripheral_subgroup wikiPageWikiLink Ambient_isotopy.
- Peripheral_subgroup wikiPageWikiLink Annals_of_Mathematics.
- Peripheral_subgroup wikiPageWikiLink Category:Algebraic_topology.
- Peripheral_subgroup wikiPageWikiLink Category:Homotopy_theory.
- Peripheral_subgroup wikiPageWikiLink Category:Knot_theory.
- Peripheral_subgroup wikiPageWikiLink Chiral_knot.
- Peripheral_subgroup wikiPageWikiLink Conjugacy_class.
- Peripheral_subgroup wikiPageWikiLink Connected_space.
- Peripheral_subgroup wikiPageWikiLink File:Granny_knot_and_square_knot.pdf.
- Peripheral_subgroup wikiPageWikiLink File:Path_from_basepoint_to_tubular_neighborhood.pdf.
- Peripheral_subgroup wikiPageWikiLink File:The_two_trefoil_knots.pdf.
- Peripheral_subgroup wikiPageWikiLink File:Tubular_neighborhood_of_knot_with_paths.pdf.
- Peripheral_subgroup wikiPageWikiLink Fundamental_group.
- Peripheral_subgroup wikiPageWikiLink Generating_set_of_a_group.
- Peripheral_subgroup wikiPageWikiLink Granny_knot_(mathematics).
- Peripheral_subgroup wikiPageWikiLink Homeomorphism.
- Peripheral_subgroup wikiPageWikiLink Invariant_theory.
- Peripheral_subgroup wikiPageWikiLink Isomorphism.
- Peripheral_subgroup wikiPageWikiLink Knot_complement.
- Peripheral_subgroup wikiPageWikiLink Knot_group.
- Peripheral_subgroup wikiPageWikiLink Knot_theory.
- Peripheral_subgroup wikiPageWikiLink Linking_number.
- Peripheral_subgroup wikiPageWikiLink Loop_(topology).
- Peripheral_subgroup wikiPageWikiLink Normal_(geometry).
- Peripheral_subgroup wikiPageWikiLink Orientation_(vector_space).
- Peripheral_subgroup wikiPageWikiLink Path_(topology).
- Peripheral_subgroup wikiPageWikiLink Pointed_space.
- Peripheral_subgroup wikiPageWikiLink Smoothness.
- Peripheral_subgroup wikiPageWikiLink Square_knot_(mathematics).
- Peripheral_subgroup wikiPageWikiLink Tangent_vector.
- Peripheral_subgroup wikiPageWikiLink Three-dimensional_space_(mathematics).
- Peripheral_subgroup wikiPageWikiLink Topological_pair.
- Peripheral_subgroup wikiPageWikiLink Trefoil.
- Peripheral_subgroup wikiPageWikiLink Tubular_neighborhood.
- Peripheral_subgroup wikiPageWikiLink Unknot.
- Peripheral_subgroup wikiPageWikiLink Wild_knot.
- Peripheral_subgroup wikiPageUsesTemplate Template:Citation.
- Peripheral_subgroup wikiPageUsesTemplate Template:MathSciNet.
- Peripheral_subgroup subject Category:Algebraic_topology.
- Peripheral_subgroup subject Category:Homotopy_theory.
- Peripheral_subgroup subject Category:Knot_theory.
- Peripheral_subgroup hypernym Subgroup.
- Peripheral_subgroup type EthnicGroup.
- Peripheral_subgroup type Mapping.
- Peripheral_subgroup comment "In algebraic topology, a peripheral subgroup for a space-subspace pair X ⊃ Y is a certain subgroup of the fundamental group of the complementary space, π1(X − Y). Its conjugacy class is an invariant of the pair (X,Y).".
- Peripheral_subgroup label "Peripheral subgroup".
- Peripheral_subgroup sameAs Q7168711.
- Peripheral_subgroup sameAs m.0k95d4t.
- Peripheral_subgroup sameAs Q7168711.
- Peripheral_subgroup wasDerivedFrom Peripheral_subgroup?oldid=704093730.
- Peripheral_subgroup isPrimaryTopicOf Peripheral_subgroup.