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- Iain Aitchison
- 2001

WE DESCRIBE a homotopy 4-sphere X4, built with the usual zero and 4-handle and two l-handles and two 2-handles (Figure 28). Of course X4 is homeomorphic to S4 [Freedman] but considerable effort has not led to a proof that X4 is diffeomorphic to S4. X4 has the following virtues: (A) Although it is easy to construct smooth homotopy 4-spheres (e.g. the Gluck… (More)

- Ian Agol, David Gabai, Iain Aitchison, Hyam Rubinstein
- 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.

Copyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyright owners. For more information on Open Research Online's data policy on reuse of materials please consult the policies page. each paper in this conference proceedings is the property of the author(s). Permission is granted to reproduce copies… (More)

- 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)

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