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