Abstract
This paper is the second in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. The top level structure of the proof is described. A compact topological space is described. Each point of this space can be described as a finite cluster of balls with additional combinatorial markings. A continuous function on this compact space is defined. It is proved that the Kepler conjecture will follow if the value of this function is never greater than a given explicit constant.
Received November 11, 1998, and in revised form September 12, 2003, and July 25, 2005. Online publication February 27, 2006.
The original version of this chapter was revised. An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-1-4614-1129-1_12
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© 2011 T.C. Hales & S.P. Ferguson
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Hales, T.C., Ferguson, S.P. (2011). A Formulation of the Kepler Conjecture. In: Lagarias, J.C. (eds) The Kepler Conjecture. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1129-1_4
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DOI: https://doi.org/10.1007/978-1-4614-1129-1_4
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