Orientations of spines of homology balls

A. Yu. Makovetskii

Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 156-162

Résumé

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 moves $M^{\pm1}$ and $L^{\pm1}$ of special spines, which do not change the manifold, are well known. We prove that $M^{+1}$ and $L^{+1}$ preserve orientability of a spine, while $M^{-1}$ and $L^{-1}$ do not. For spines of homology balls, a class of moves is described which allow one to pass from a given orientation of a spine to any other orientation of the spine.