Figure 1:
The curve is covered by coordinate patches , with transition functions . The composition is the holonomy of the curve. 

Figure 2:
The ADM decomposition is based on the Lorentzian version of the Pythagoras theorem. 

Figure 3:
Three tetrahedra can occur in Lorentzian dynamical triangulation. 

Figure 4:
A manifold with a single boundary describes the birth of a universe in the HartleHawking approach to quantum cosmology. 
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