# HELP! Why CS is topological? Why BF is topological?

1. Feb 19, 2008

### astros

Hello,
I know that the CS Lagrangian is a topological invariant, in the sense that it does not depend on the connection we choose. OK, but a TFT is a field theory whose Lagrangian and all other observables do not depend on the metric, a connection in general is not uniquely defined by a metric! Then how can I see CS theory as topological? Another problem, CS Lagrangian is a 3-forme, normally; a Lagrangian must be a scalar!? After that, can I see that CS is topological by showing that the number of constraints is equal to the number of degrees of freedom? If yes HOW! The same for BF! Please help me RANI N’NAGER!!!

2. Feb 21, 2008

nobody!!!