If $f\colon M\to\R^3$ is a tight immersion, then
$M$ can be decomposed into two regions, $M^+$ and $M^$ where:
 $K\ge 0$ on $M^+$ and
$K\le 0$ on $M^$
 $f$ embeds $M^+$ onto
the complement in $\dHf$ of a finite number of
disjoint planar convex closed disks
$D_1,\ldots,D_k$ in $\dHf$
 for each $i$,
$f^{1}(\partial D_i)$ is a nontrivial 1cycle in
$M$
(these are called top cycles)
