Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners / / by Thomas Kerler, Volodymyr V. Lyubashenko

• Autore: Kerler Thomas
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001
• Edizione: 1st ed. 2001.
• Descrizione fisica: 1 online resource (VI, 383 p.)
• Disciplina: 510 s; 530.14/3
• Soggetto topico: Commutative 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
• Classificazione: 81T05; 57N10; 18D05
• Persona (resp. second.): LyubashenkoVolodymyr V
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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).
• Titolo autorizzato: Non-semisimple topological quantum field theories for 3-manifolds with corners
• ISBN: 3-540-44625-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910144598203321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 1617-9692 ; ; 1765