{"product_id":"nonsemisimple-topological-quantum-field-theories-for-3manifolds-with-corners-lecture-notes-in-mathematics-1765","title":"NonSemisimple Topological Quantum Field Theories for 3Manifolds with Corners (Lecture Notes in Mathematics, 1765)","description":"\u003cp\u003ed + 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 Atiyahs 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).\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Default Title","offer_id":45885529227462,"sku":"DADAX3540424164","price":67.76,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0695\/9389\/1014\/files\/61Yu1YDeUfL.jpg?v=1779869050","url":"https:\/\/ergodemedia.com\/products\/nonsemisimple-topological-quantum-field-theories-for-3manifolds-with-corners-lecture-notes-in-mathematics-1765","provider":"Ergodemedia","version":"1.0","type":"link"}