01806nam 2200565Ia 450 991045242720332120200520144314.01-60876-873-2(CKB)2550000001041690(EBL)3018869(SSID)ssj0000835855(PQKBManifestationID)11502838(PQKBTitleCode)TC0000835855(PQKBWorkID)11008472(PQKB)10583072(MiAaPQ)EBC3018869(Au-PeEL)EBL3018869(CaPaEBR)ebr10661808(OCoLC)847647151(EXLCZ)99255000000104169020090128d2009 uy 0engur|n|---|||||txtccrOcean circulation and El Nino[electronic resource] new research /John A. Long and David S. Wells, editorsNew York Nova Science Publishersc20091 online resource (305 p.)Description based upon print version of record.1-60692-084-7 Includes bibliographical references and index.Ocean currentsResearchPacific OceanOcean circulationResearchPacific OceanMeridional overturning circulationResearchEl Nino CurrentResearchElectronic books.Ocean currentsResearchOcean circulationResearchMeridional overturning circulationResearch.551.46/2Long John A728919Wells David S938989MiAaPQMiAaPQMiAaPQBOOK9910452427203321Ocean circulation and El Nino2116587UNINA04607nam 22007935 450 991014459820332120250724093327.03-540-44625-710.1007/b82618(CKB)1000000000233213(SSID)ssj0000325259(PQKBManifestationID)12116390(PQKBTitleCode)TC0000325259(PQKBWorkID)10321702(PQKB)11155557(DE-He213)978-3-540-44625-5(MiAaPQ)EBC3071724(PPN)155196944(BIP)7336004(EXLCZ)99100000000023321320121227d2001 u| 0engurnn#008mamaatxtccrNon-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners /by Thomas Kerler, Volodymyr V. Lyubashenko1st ed. 2001.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2001.1 online resource (VI, 383 p.)Lecture Notes in Mathematics,1617-9692 ;1765Bibliographic Level Mode of Issuance: Monograph3-540-42416-4 Includes bibliographical references and index.and Summary of Results -- The Double Category of Framed, Relative 3-Cobordisms -- Tangle-Categories and Presentation of Cobordisms -- Isomorphism between Tangle and Cobordism Double Categories -- Monoidal categories and monoidal 2-categories -- Coends and construction of Hopf algebras -- Construction of TQFT-Double Functors -- Generalization of a modular functor -- From Quantum Field Theory to Axiomatics -- Double Categories and Double Functors -- Thick tangles.d + 1-dimensional manifold, whose is a union of d-dimensional boundary disjoint v manifolds and d, a linear : -+ The manifold -Zod V(Md+l) V(Zod) V(Zld). ma- is with the orientation. The axiom in that z0g, Zod opposite gluing [Ati88] requires if we two such d + 1-manifolds a common d-subma- glue together along (closed) fold of in their the linear for the has to be the boundaries, composite compo- map tion of the linear of the individual d + 1-manifolds. maps the of and as in we can state categories functors, [Mac88], Using language axioms as follows: concisely Atiyah's very Definition 0.1.1 A in dimension d is a ([Ati88]). topological quantumfield theory between monoidal functor symmetric categories [Mac881 asfollows: V : --+ k-vect. Cobd+1 finite Here k-vect denotes the whose are dimensional v- category, objects for field tor over a field k, which we assume to be instance, a perfect, spaces The of of characteristic 0. set between two vector is morphisms, simply spaces the set of linear with the usual The has as composition. category Cobd+1 maps manifolds. such closed oriented d-dimensional A between two objects morphism. Zd d oriented d 1-- d-manifolds and is a + 1-cobordism, an + Zod meaning gMd+l = Zd is the d- mensional manifold, Md+l, whose Lj boundary _ZOd of the d-manifolds. consider union two we as joint (Strictly speaking morphisms cobordisms modulo relative Given another or homeomorphisms diffeomorphisms).Lecture Notes in Mathematics,1617-9692 ;1765Commutative algebraCommutative ringsAlgebra, HomologicalManifolds (Mathematics)Mathematical physicsCommutative Rings and AlgebrasCategory Theory, Homological AlgebraManifolds and Cell ComplexesTheoretical, Mathematical and Computational PhysicsCommutative algebra.Commutative rings.Algebra, Homological.Manifolds (Mathematics)Mathematical physics.Commutative Rings and Algebras.Category Theory, Homological Algebra.Manifolds and Cell Complexes.Theoretical, Mathematical and Computational Physics.510 s530.14/381T05msc57N10msc18D05mscKerler Thomasauthttp://id.loc.gov/vocabulary/relators/aut53255Lyubashenko Volodymyr Vauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910144598203321Non-semisimple topological quantum field theories for 3-manifolds with corners262224UNINA