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The prediction of non-trivial topological phases in Bloch insulators in threedimensions has recently been experimentally verified. Here, I provide a picturefor obtaining the $Z_{2}$ invariants for a three dimensional topologicalinsulator by deforming suitable 2d planes in momentum space and by using aformula for the 2d $Z_{2}$ invariant based on the Chern number. The physicalinterpretation of this formula is also clarified through the connection betweenthis formulation of the $Z_{2}$ invariant and the quantization of spin Hallconductance in two dimensions.

Characterization of 3d topological insulators by 2d invariants