Topological Quasi-Particles

Abstract

The subject of topology is the set of properties of relative positions that can be defined without the use of metric properties. A metric induces a particular topology only locally, and a metric is not necessary to define a topology. In the familiar metric geometry, equivalence is constructed by maps that conserve distances. In topology, equivalence is constructed by maps that conserve neighbourhood or continuity. Even in the simplest spatially flat case, there exist topologically inequivalent cosmological models that do not differ in their metrical properties [2,3]. The unexpectedly low amplitudes of the quadrupole and octupole components of the cosmic microwave background have led to the proposal of a dodecahedral topology of space [6,7,12].