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Wir sind gerne für Sie dad + 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).
Produkteigenschaften
- Artikelnummer: 9783540424161
- Medium: Buch
- ISBN: 978-3-540-42416-1
- Verlag: Springer Berlin Heidelberg
- Erscheinungstermin: 11.09.2001
- Sprache(n): Englisch
- Auflage: 2001
- Serie: Lecture Notes in Mathematics
- Produktform: Kartoniert
- Gewicht: 593 g
- Seiten: 383
- Format (B x H x T): 155 x 235 x 22 mm
- Ausgabetyp: Kein, Unbekannt