TYPE OF 3-MANIFOLDS AND ADDITION OF RELATIVISTIC KINKS

Abstract

The type of a closed, connected, orientable 3-manifold M was first considered in the classification of relativistic kinks over the space-time 4-manifold M × R. In this paper theorems are developed relating the type of M to H1 (M; Z), which lead to the determination of the type of large families of 3-manifolds. The relation of type to connected sum is established, and the connected sum is also used to define addition of kinks. The kink addition is related to the sum of the kink numbers, as well as addition in the bordism group Ω3(P3).