Year: 2013
Type: article
Abstract: We prove that the 8 4 2 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps.Its volume is twice the volume V 8 of the ideal regular octahedron; that is, 7.32 . . .= 2V 8 .The proof relies on Agol's argument used to determine the minimal volume hyperbolic 3-manifolds with 2 cusps.We also need to estimate the volume of a hyperbolic 3-manifold with totally geodesic boundary which contains an essential surface with nonseparating boundary.• In the case where n = 0 (closed manifold), Gabai, Meyerhoff and Milley [2009] showed that the Weeks manifold has the minimal volume.Its volume is 0.94. . . .• In the case where n = 1, Cao and Meyerhoff [2001] showed that the figure-eight knot complement and the manifold obtained by the (5, 1)-Dehn surgery from the Whitehead link
Source: Pacific Journal of Mathematics
Author: Ken’ichi Yoshida
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2089135648