Space-time topology as a consequence of the dynamics of closed boson strings. I. The zeroth and first approximations

The possibility of constructing a theory in which the space-time topology is determined by the dynamics of closed boson strings is analyzed. The initial object in the theory is a topological space of the contours which determines the form of the string interaction vertex. A cohomological complex and a topologically invariant action are constructed on the space of contours. The equations of motion obtained by varying the action coincide with the condition of closure of differential cohomology forms. The analysis is carried out in the form of an expansion with respect to the string coupling constant. The zeroth- and firstorder approximations are considered. Restrictions imposed on the space-time topology by the string dynamics are found. In what follows, by the space-time is meant an intermediate finite-dimensional space obtained from the original infinite-dimensional space of the contours and containing singularities. To pass to a smooth physical space-time it is necessary to pass to the massless limit, which will be the subject of another paper.