Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners

2001
ISBN: 978-3-540-42416-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1765, 383 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 593 g

Reihe: Lecture Notes in Mathematics

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).

Zielgruppe

Research

Autoren/Hrsg.

Lyubashenko, Volodymyr V.

Kerler, Thomas

Fachgebiete

• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

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.