#
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.

http://www.tac.mta.ca/tac/volumes/18/10/18-10.dvi

http://www.tac.mta.ca/tac/volumes/18/10/18-10.ps

http://www.tac.mta.ca/tac/volumes/18/10/18-10.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/10/18-10.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/10/18-10.ps

TAC Home