Four-dimensional kinks

The homotopy classes of Lorentz signature metric tensor fields on parallelisable four-manifolds are classified for both compact and non-compact manifolds. It is demonstrated that the homotopy classes form Abelian groups whose generators correspond to generalised elementary 'kinks', and their extension structures are analysed. It is also demonstrated that all odd kink states have the fermionic property of being odd under 3600 rotations. Speculations on the physical interpretation of four-dimensional kink states are made which generalise those of Shastri, Williams and Zvengrowski (Int. J. Theor. Phys.; 19:1 (1980)) from three to four dimensions. (author)