Two-critical-point obstruction to a trivial cobordism (source code)

= Two-critical-point obstruction to a trivial cobordism
{title2=$\mu=\lambda+1,\quad S_U(p)\cdot S_L(q)=\pm1$}

If a <cobordism Morse function> on a <trivial cobordism> has exactly two <critical points>, its relative <Morse chain complex> has two generators and must be acyclic. Their indices therefore differ by one. The only differential is multiplication by the signed intersection of the lower point's <belt sphere> with the higher point's <attaching sphere> in a common regular level. A two-term complex of copies of $\mathbb Z$ is acyclic exactly when that integer is a unit. Algebraic intersection is therefore a necessary condition; it is not by itself a geometric handle-cancellation statement.