Nov. 26, 2007

Ian Agol

Survey on volumes of hyperbolic 3-orbifolds and manifolds

A hyperbolic n-orbifold is a quotient of n-dimensional hyperbolic space by a discrete group of isometries. Jorgensen and Thurston proved that the volumes of hyperbolic 3-orbifolds form a well-ordered set. Recently, the minimal volume 3-orbifolds and minimal volume orientable 3-manifolds have been identified. The smallest volume manifold is known as the Weeks-Matveev-Fomenko manifold, with volume .9427..., and has been conjectured to be minimal volume since the '80s. We'll survey these topics, and indicate some of the techniques that go into proving them.

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