Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Knot_theory> ?p ?o }
- Knot_theory abstract "In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3 (in topology, a circle isn't bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.Knots can be described in various ways. Given a method of description, however, there may be more than one description that represents the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram. Any given knot can be drawn in many different ways using a knot diagram. Therefore, a fundamental problem in knot theory is determining when two descriptions represent the same knot.A complete algorithmic solution to this problem exists, which has unknown complexity. In practice, knots are often distinguished by using a knot invariant, a \"quantity\" which is the same when computed from different descriptions of a knot. Important invariants include knot polynomials, knot groups, and hyperbolic invariants.The original motivation for the founders of knot theory was to create a table of knots and links, which are knots of several components entangled with each other. Over six billion knots and links have been tabulated since the beginnings of knot theory in the 19th century.To gain further insight, mathematicians have generalized the knot concept in several ways. Knots can be considered in other three-dimensional spaces and objects other than circles can be used; see knot (mathematics). Higher-dimensional knots are n-dimensional spheres in m-dimensional Euclidean space.".
- Knot_theory thumbnail Trefoil_knot_arb.png?width=300.
- Knot_theory wikiPageExternalLink ReducedKnotDiagram.html.
- Knot_theory wikiPageExternalLink ReducibleCrossing.html.
- Knot_theory wikiPageExternalLink on_vortex_atoms.html.
- Knot_theory wikiPageExternalLink books?id=BLvGkIY8YzwC.
- Knot_theory wikiPageExternalLink books?id=DJHI7DpgIbIC.
- Knot_theory wikiPageExternalLink books?id=PhHhw_kRvewC.
- Knot_theory wikiPageExternalLink books?id=ebd6QofqY6QC&pg=PA203.
- Knot_theory wikiPageExternalLink books?id=fSKrRQ77FMkC.
- Knot_theory wikiPageExternalLink books?id=naYJBAAAQBAJ.
- Knot_theory wikiPageExternalLink books?id=sh3uWYLfozsC.
- Knot_theory wikiPageExternalLink knotplot.com.
- Knot_theory wikiPageExternalLink ~knotinfo.
- Knot_theory wikiPageExternalLink knots.
- Knot_theory wikiPageExternalLink smoke%20rings.mpg.
- Knot_theory wikiPageID "153008".
- Knot_theory wikiPageLength "42236".
- Knot_theory wikiPageOutDegree "166".
- Knot_theory wikiPageRevisionID "703691612".
- Knot_theory wikiPageWikiLink 3-manifold.
- Knot_theory wikiPageWikiLink A._Caudron.
- Knot_theory wikiPageWikiLink Alexander_polynomial.
- Knot_theory wikiPageWikiLink Alexandre-Théophile_Vandermonde.
- Knot_theory wikiPageWikiLink Algorithm.
- Knot_theory wikiPageWikiLink Alternating_knot.
- Knot_theory wikiPageWikiLink Ambient_isotopy.
- Knot_theory wikiPageWikiLink Analysis_of_algorithms.
- Knot_theory wikiPageWikiLink Associative_property.
- Knot_theory wikiPageWikiLink Atom.
- Knot_theory wikiPageWikiLink Book_of_Kells.
- Knot_theory wikiPageWikiLink Borromean_rings.
- Knot_theory wikiPageWikiLink Braid_theory.
- Knot_theory wikiPageWikiLink Carl_Friedrich_Gauss.
- Knot_theory wikiPageWikiLink Category:Knot_theory.
- Knot_theory wikiPageWikiLink Celtic_Christianity.
- Knot_theory wikiPageWikiLink Celtic_knot.
- Knot_theory wikiPageWikiLink Chinese_knotting.
- Knot_theory wikiPageWikiLink Chiral_knot.
- Knot_theory wikiPageWikiLink Chirality_(chemistry).
- Knot_theory wikiPageWikiLink Circle.
- Knot_theory wikiPageWikiLink Commutative_property.
- Knot_theory wikiPageWikiLink Contact_geometry.
- Knot_theory wikiPageWikiLink Continuous_function.
- Knot_theory wikiPageWikiLink Crossing_number_(knot_theory).
- Knot_theory wikiPageWikiLink DNA.
- Knot_theory wikiPageWikiLink Digon.
- Knot_theory wikiPageWikiLink Dimension.
- Knot_theory wikiPageWikiLink Dowker_notation.
- Knot_theory wikiPageWikiLink Edward_Witten.
- Knot_theory wikiPageWikiLink Embedding.
- Knot_theory wikiPageWikiLink Endless_knot.
- Knot_theory wikiPageWikiLink Euclidean_space.
- Knot_theory wikiPageWikiLink File:Knot_table.svg.
- Knot_theory wikiPageWikiLink Finite_type_invariant.
- Knot_theory wikiPageWikiLink Floer_homology.
- Knot_theory wikiPageWikiLink Fundamental_group.
- Knot_theory wikiPageWikiLink Garland_Baird_Briggs.
- Knot_theory wikiPageWikiLink Geodesic.
- Knot_theory wikiPageWikiLink Geometrization_conjecture.
- Knot_theory wikiPageWikiLink Homeomorphism.
- Knot_theory wikiPageWikiLink Homology_(mathematics).
- Knot_theory wikiPageWikiLink Hopf_link.
- Knot_theory wikiPageWikiLink Horosphere.
- Knot_theory wikiPageWikiLink Hyperbolic_geometry.
- Knot_theory wikiPageWikiLink Hyperbolic_link.
- Knot_theory wikiPageWikiLink Immersion_(mathematics).
- Knot_theory wikiPageWikiLink Injective_function.
- Knot_theory wikiPageWikiLink Integer.
- Knot_theory wikiPageWikiLink James_Waddell_Alexander_II.
- Knot_theory wikiPageWikiLink John_Horton_Conway.
- Knot_theory wikiPageWikiLink Jones_polynomial.
- Knot_theory wikiPageWikiLink Knot.
- Knot_theory wikiPageWikiLink Knot_(mathematics).
- Knot_theory wikiPageWikiLink Knot_complement.
- Knot_theory wikiPageWikiLink Knot_group.
- Knot_theory wikiPageWikiLink Knot_invariant.
- Knot_theory wikiPageWikiLink Knot_polynomial.
- Knot_theory wikiPageWikiLink Kurt_Reidemeister.
- Knot_theory wikiPageWikiLink Link_(knot_theory).
- Knot_theory wikiPageWikiLink Linking_number.
- Knot_theory wikiPageWikiLink List_of_knot_theory_topics.
- Knot_theory wikiPageWikiLink List_of_prime_knots.
- Knot_theory wikiPageWikiLink Luminiferous_aether.
- Knot_theory wikiPageWikiLink Max_Dehn.
- Knot_theory wikiPageWikiLink Maxim_Kontsevich.
- Knot_theory wikiPageWikiLink Molecular_knot.
- Knot_theory wikiPageWikiLink N-sphere.
- Knot_theory wikiPageWikiLink Orientation_(vector_space).
- Knot_theory wikiPageWikiLink Perko_pair.
- Knot_theory wikiPageWikiLink Peter_Tait_(physicist).
- Knot_theory wikiPageWikiLink Physical_knot_theory.
- Knot_theory wikiPageWikiLink Piecewise_linear_manifold.
- Knot_theory wikiPageWikiLink Polynomial.
- Knot_theory wikiPageWikiLink Prime_knot.
- Knot_theory wikiPageWikiLink Prime_number.
- Knot_theory wikiPageWikiLink Quantum_field_theory.
- Knot_theory wikiPageWikiLink Quantum_group.
- Knot_theory wikiPageWikiLink Quantum_invariant.
- Knot_theory wikiPageWikiLink Quantum_topology.