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Interesting Kirby diagrams of the 4-sphere?
by
Dubravko Ivansic
The George Washington University
There exist hyperbolic manifolds obtained by pairing sides of a hyperbolic polyhedron that are complements of 5 tori in the 4-sphere. Using the construction of the hyperbolic manifold one can get a complicated Kirby diagram for the 4-sphere, with dozens of 1- and 2-handles. While this diagram is equivalent via Kirby moves to the diagram of the standard differentiable 4-sphere, its complicatedness seems to suggest that a counterexample to the differentiable Poincare conjecture in dimension 4 could be very involved indeed.
Date received: December 12, 2001
Copyright © 2001 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caip-07.