SOME PROBLEMS OF TOPOLOGY CHANGE DESCRIPTION IN THE THEORY OF SPACETIME

The problem of topology change description in gravitation theory is analyzed in details. It is pointed out that in standard four-dimensional theories the topology of space may be considered as a particular case of the boundary conditions (or constraints). Therefore to describe the changes of space or spacetime topology the number of the coordinate maps, the order of their junction and the junction conditions must be converted from the class of constraints or boundary data into the class of dynamical variables. In the framework of four-dimensional theory this problem cannot be solved in its general formulation, while it is possible to describe the changes of three-space topology on the given four-manifold. In the framework of multidimensional theories the space (and spacetime) may be considered as the embedded manifolds. It gives the real possibilities both for the dynamical description of the topology of space or spacetime and for the description of the topology changes of general kind.