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Zap. Nauchn. Sem. POMI, 2000 Volume 267, Pages 156–162 (Mi znsl1273)

Orientations of spines of homology balls

A. Yu. Makovetskii

Chelyabinsk State University

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 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.

UDC: 515.162.3

Received: 29.10.1999


 English version:
Journal of Mathematical Sciences (New York), 2003, 113:6, 818–821

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© Steklov Math. Inst. of RAS, 2024