Orientations of Spines of Homology Balls

Abstract

Oriented special spines of 3-manifolds are studied. (Orientation is an additional structure on the spine, and each 3-manifold possesses a special spine with such a structure.) The transformations (moves) $M^{{\text{ }} \pm {\text{1}}}$ and $L^{{\text{ }} \pm {\text{1}}}$ of special spines, which do not change the manifold, are well known. It is proved that $M^{{\text{ + 1}}}$ and $L^{{\text{ + 1}}}$ preserve orientability of a spine, while $M^{{\text{ }} - {\text{1}}}$ and $L^{{\text{ }} - {\text{1}}}$ do not. For spines of homology balls, a class of moves is described allowing one to pass from a given orientation of a spine to any other orientation of the spine. Bibliography: 6 titles.