 Topological quantum field theory partition function

The scalar assigned to a closed spacetime manifold by a topological quantum field theory. Gluing the two ends of a cylinder over a spatial manifold $\Sigma$ gives $Z(\Sigma \times S^1)=\mathrm{tr}(1_{V(\Sigma )})=\dim V(\Sigma )$. This is the ground-state degeneracy when the state space describes the topological ground sector of a gapped system.