Key points are not available for this paper at this time.
closed fake surface P is called a standard spine of a closed 3-manifold M, if it is embedded in M and M-N (P) is homeomorphic to a 3-ball (N (P) denotes a regular neighborhood of P in M). It is known (2) that any closed 3-manifold has a standard spine.
Ippei Ishii (Mon,) studied this question.