Morse theory and central configurations in the spatial \(N\)-body problem. (English) Zbl 1152.70009
Summary: In the spirit of J. Palmore [Bull. Am. Math. Soc. 79, 904–908 (1973; Zbl 0273.57016)] and F. Pacella [Arch. Ration. Mech. Anal. 97, 59–74 (1987; Zbl 0627.58013)], Morse theory is used to obtain a lower bound for the number of central configurations in the spatial \(N\)-body problem. The homology of the configuration ellipsoid with the collision and collinear manifolds removed and the \(SO(3)\) symmetry quotiented out is calculated. As intermediate steps, homology calculations are carried out for several additional manifolds naturally arising in the \(N\)-body problem.
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