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The classical Chern-Simons invariant is the basis for a 3-dimensional topological quantum field theory. We describe some of the mathematical structure which has been built around this and other topological field theories. We include, in the introduction and the last section, some general discussion about the current interaction between geometry and quantum theories of fields and gravity.doi:10.1090/s0273-0979-09-01243-9 fatcat:ge6rjrpv2bhv5frdgmtgmqxmzi