Classically, tightness is defined in terms of the total absolute
curvature:
\tau(f)={1\over 2\pi}\int_M |K|\,dA.
It is possible to show that $\tau(f)\ge 4-\chi(M)$,
and when equality holds, $f$ is tight.
This definition is only valid for smooth immersions, but the
two-piece property makes sense even in the polyhedral case.
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