Geodesic
Towards an n-category of cobordisms
Theory and applications of categories, Tome 18 (2007), pp. 274-302

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We discuss an approach to constructing a weak n-category of cobordisms. First we present a generalisation of Trimble's definition of n-category which seems most appropriate for this construction; in this definition composition is parametrised by a contractible operad. Then we show how to use this definition to define the n-category nCob, whose k-cells are k-cobordisms, possibly with corners. We follow Baez and Langford in using ``manifolds embedded in cubes'' rather than general manifolds. We make the construction for 1-manifolds embedded in 2- and 3-cubes. For general dimensions k and n we indicate what the construction should be.

Classification : 18A05, 18D05, 18D10, 18D50, 57R90
Keywords: n-category, operad, topological quantum field theory, cobordism 
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     author = {Eugenia Cheng and Nick Gurski},
     title = {Towards an n-category of cobordisms},
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     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/TAC_2007_18_a9/}
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Eugenia Cheng; Nick Gurski. Towards an n-category of cobordisms. Theory and applications of categories, Tome 18 (2007), pp. 274-302. http://geodesic.mathdoc.fr/item/TAC_2007_18_a9/