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- Ian Agol, David Gabai, Iain Aitchison, Hyam Rubinstein, Oliver Goodman
- 2002

T T T T T T T T T T T T T T T Abstract Given a hyperbolic 3–manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable hyperbolic 3–manifold has volume > .32.

- Iain R. Aitchison, J. Hyam Rubinstein
- Experimental Mathematics
- 1997

- I. R. AITCHISON
- 1999

It is known that about 70% of surgeries on the figure 8 knot give manifolds which contain immersed incompressible surfaces. We improve this to about 80% by giving a very simple proof that all even surgeries give manifolds containing such a surface. Moreover, we give a quick proof that every (6k, t) surgery is virtually Haken, thereby partially dealing with… (More)

- DANIEL S. SILVER, Iain R. Aitchi, Iain R. Aitchison, D. S. SILVER
- 2010

Construction by isotopy is a technique introduced by Iain R. Aitchison for obtaining doubly slice fibered knots in any dimension. We show that if k is any doubly slice fibered (n 2)-knot, n > 5 , such that nx (Sn k) = Z , then k is constructible by isotopy. We also prove that the m-twist-spin of any doubly slice knot is constructible by isotopy.… (More)

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