Where Topological Torsion is a feature of three or more dimensions, Topological
Parity is a property of four or more dimensions. An argument can be made that
Topological Parity cannot be zero in irreversible systems, Therefore, turbulent
hydrodynamic flows must have none null Topological Parity. In electromagnetic
systems, a non-zero value of E.B, the second Poincare invariant, is a signature
of Topological Parity. In field theories of elementary particles, such effects
lead to the breaking of parity symmetry
The arguments above apply to a 4 dimensional variety, like space time, but the concepts can be extended to N forms dA^dA... and N-1 forms A^dA...