On a volume invariant of 3-manifolds
arxiv(2024)
摘要
This paper investigates a real-valued topological invariant of 3-manifolds
called topological volume. For a given 3-manifold M it is defined as the
smallest volume of the complement of a (possibly empty) hyperbolic link in M.
Various refinements of this invariant are given, asymptotically tight upper and
lower bounds are determined, and all non-hyperbolic closed 3-manifolds with
topological volume of at most 3.07 are classified. Moreover, it is shown that
for all but finitely many lens spaces, the volume minimiser is obtained by Dehn
filling one of the cusps of the complement of the Whitehead link or its sister
manifold.
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