Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
(Sprache: Englisch)
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...
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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).
Inhaltsverzeichnis zu „Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners “
- Introduction and summary of results- The double category of framed, relative 3-cobordisms
- Tangle-categories and presentation of cobordisms
- Isomorphism between tangle and cobordism categories
- Monoidal categories and monoidal 2-categories
- Coends and construction of Hopf algebras
- Construction of TQFT-Double Functors
- Generalization of modular functor
- A: From quantum field theory of axiomatics
- B: Double categories and double functors
- C: Thick tangles
Bibliographische Angaben
- Autoren: Volodymyr V. Lyubashenko , Thomas Kerler
- 2001, 392 Seiten, Maße: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer Berlin Heidelberg
- ISBN-10: 3540424164
- ISBN-13: 9783540424161
- Erscheinungsdatum: 11.09.2001
Sprache:
Englisch
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