Top Cycle:

Given a tight immersion of a surface M in space, suppose a top set, S, is not contained in a line. Then the convex hull of S is a closed 2-dimensional disk, and its boundary is a convex curve c in M. If S is not itself convex, then c does not bound a region in M and in this case, c is called a top cycle of M.

The top cycles play a crucial role in the study if tight immersions, and in particular, they form the boundaries of an important decomposition of a tight surface into two regions with special geometric properties.

See also:

[More] Top sets and top cycles
[More] Tightness and the convex hull

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8/12/94 dpvc@geom.umn.edu -- The Geometry Center