Configuration Spaces of Sn+1, n > 1
The configuration spares of spheres, as to be expected, are intimately related to those of the Euclidean spaces of the same dimension. Nevertheless, they present important novel features. The primary difference is due to the fact that the tangent bundle of the sphere is nontrivial except for the cases when the sphere S m is S 1, S 3, or S 7. In this chapter we consider the case m > 2 only, so the relevant configuration spaces are simply connected. The case S 2 presents a new kind of difficulty, as the corresponding configuration spaces are no longer simply connected. It will be taken up in Chapter IV.
KeywordsSymmetric Group Tangent Bundle Configuration Space Homotopy Class Stereographic Projection
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