Memoirs of the American Mathematical Society 1998; 91 pp; softcover Volume: 132 ISBN10: 0821806920 ISBN13: 9780821806920 List Price: US$46 Individual Members: US$27.60 Institutional Members: US$36.80 Order Code: MEMO/132/628
 The phase space of the spatial threebody problem is an open subset in \({\mathbb R}^{18}\). Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the wellknown bifurcations due to central configurations, and three are due to "critical points at infinity". This disproves Birkhoff's conjecture that the bifurcations occur only at central configurations. Readership Graduate students and research mathematicians and physicists working in celestial mechanics. Table of Contents  Introduction
 The decomposition of the spaces
 The cohomology
 The analysis of \({\mathfrak K}(c,h)\)for equal masses
 The analysis of \({\mathfrak K}(c,h)\) for general masses
 Bibliography
