= Perfect Morse function
{c}
{title2=$c_i=b_i$}
A <Morse function> is perfect over a specified field when its numbers of <critical points> equal the <Betti numbers> over that field. Over the rationals this forces every integer <matrix> in its <Morse chain complex> to have rank zero, hence to vanish. Consequently its integral <homology> is free of rank $c_i$ in every degree; a <manifold> with integral <homology> torsion cannot admit such an integral-critical-count perfect function.
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