High-dimensional Knot Theory

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:appliesTo	differential topology manifold theory
gptkbp:concerns	embeddings of spheres in higher-dimensional spaces
gptkbp:developedBy	gptkb:Stephen_Smale gptkb:John_Milnor gptkb:Michel_Kervaire
https://www.w3.org/2000/01/rdf-schema#label	High-dimensional Knot Theory
gptkbp:notableAchievement	gptkb:h-cobordism_theorem gptkb:Donaldson's_theorem gptkb:Kervaire-Milnor_classification gptkb:Kervaire_invariant gptkb:s-cobordism_theorem gptkb:Casson_invariant gptkb:Pontryagin_classes gptkb:Whitney_trick gptkb:Stiefel-Whitney_classes gptkb:Alexander_duality gptkb:Rokhlin_invariant gptkb:Generalized_knot_groups gptkb:Homotopy_spheres gptkb:Knot_cobordism_group gptkb:Knot_concordance_group gptkb:Levine's_algebraic_classification gptkb:Milnor's_invariants gptkb:Surgery_exact_sequence gptkb:Wall's_surgery_theory Exotic smooth structures Freedman's work on 4-manifolds Intersection forms Knot cobordism invariants Knot complements in higher dimensions Knot group generalizations Linking forms Smale's work on spheres classification of high-dimensional knots
gptkbp:relatedTo	gptkb:topology knot theory
gptkbp:studies	gptkb:exotic_spheres knot invariants knot cobordism knot concordance knots in dimensions higher than three n-dimensional knots
gptkbp:uses	gptkb:topology homotopy theory surgery theory cobordism theory
gptkbp:bfsParent	gptkb:Andrew_Ranicki
gptkbp:bfsLayer	6