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

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

by Thomas Kerler , Volodymyr V. Lyubashenko
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Book cover type: Paperback
  • ISBN13: 9783540424161
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 383
  • Original Price: USD 54.99
  • Language: English
  • Edition: 2001
  • Item Weight: 549 grams
  • BISAC Subject(s): Waves & Wave Mechanics

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).

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