A computer search for contractible 3-manifolds |
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| Authors: | David Gillman Peter Laszlo |
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| Affiliation: | University of California, Los Angeles, CA 90024, USA;California State Polytechnic University, Pomona, CA 91768, USA |
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| Abstract: | A theorem is proved giving a necessary condition for a standard spine of a prime homology 3-ball to be minimal. This result enables an inspection of all standard spines with five or fewer vertices, by computer. There are exactly two such minimal spines, one for the 3-ball and one for the dodecahedral homology-ball of Poincaré. Corollary: No counterexample to the Poincaré Conjecture exists having a standard spine with five or fewer vertices. |
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| Keywords: | 57M20 57M40 57N12 |
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