Existence results of $$\text {Spin}(2, n - 1)_0$$ -pseudo-Riemannian cobordisms

Abstract

In this note, we study necessary and sufficient conditions for the existence of a Spin\((n + 1)\)-dimensional cobordism that supports a non-singular and non-degenerate pseudo-Riemannian metric of signature \((2, n - 1)\), which restricts to a non-singular time-orientable Lorentzian metric on its boundary. The corresponding cobordism groups are computed.