Making Surfaces Tight

A surface may have points that can be cut off in pairs, so it is not tight.
Strategy:
  • Place a big ball around the surface.
  • Attach tubes from the ball to all points that could be cut off.

(The ball is the M^+ region. The tubes are attached at the disks D_i.)

Note that this changes the topology:
  • The first tube forms a connected sum with the sphere
  • The remaining tubes add handles

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