First Singular Homology Group of Spacetime

Abstract

The mathematical structure of Minkowski space, a consequence of the postulates of the special theory of relativity, is endowed with several physically important non-Euclidean topologies defined using the causal structure of spacetime. The present paper is devoted to the study of the first singular homology group of the Minkowski space with one such topology, namely the t-topology, using the relationship between the fundamental group and the first singular homology group for path connected spaces. A similar study has also been carried out for a Lorentz manifold with the path topology.