Trivial cobordism
= Trivial cobordism
{title2=$M\times[0,1]$}
A <cobordism> is trivial when it is <diffeomorphic> to a cylinder with the prescribed incoming boundary identification. Both boundary inclusions are <homotopy equivalences> and its <relative homology> with respect to either end vanishes. It can have <critical points> for a chosen <cobordism Morse function>; those must form an acyclic relative <Morse chain complex>.