Towards an n-category of cobordisms

Eugenia Cheng and Nick Gurski

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.

Keywords: n-category, operad, topological quantum field theory, cobordism

2000 MSC: 18A05, 18D05, 18D10, 18D50, 57R90

Theory and Applications of Categories, Vol. 18, 2007, No. 10, pp 274-302.

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