Polyhedral Deformations of a Cone Manifold
Vol. 13 (2006), No. 3, Page 259--275.
AALAM, A.
Polyhedral Deformations of a Cone Manifold
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Abstract:
A single parameter family of polyhedra $P(\psi)$ is constructed in three dimensional spaces of constant curvature $C(\psi)$. Identification of the faces of the polyhedra via isometries results in cone manifolds $M(\psi)$ which are topologically $S^1\times S^2$, $S^3$ or singular $S^2$ . The singular set of $M(\psi)$ can have vertices of degree three for some values of $\psi$ and can also be the Whitehead link or form other configurations. Curvature varies continuously with $\psi$. At $\psi=0$ spontaneous surgery occurs and the topological type of $M(\psi)$ changes. This phenomenon is described.
Mathematics Subject Classification (2000): 57M50.
Mathematical Reviews Number: MR2284405
Received: 2005-08-11
