The volume of a unit sphere in this many dimensions is pi squared over two.
This is the only dimension for which the smooth Poincare conjecture has not been resolved and the only dimension for which R to the n has an exotic smooth structure. In this many dimensions, isomorphisms of piecewise linear and smooth manifolds are the same, but different from isomorphisms of topological manifolds. The Hopf fibration is a map from a sphere in this many dimensions to a sphere in one fewer dimensions. This is the dimension of an algebra denoted (*) H for its discoverer, Hamilton. The volume of a unit sphere in this many dimensions is pi squared over two. This is the minimum number of dimensions in which the Klein bottle can be embedded with no self-intersections. Minkowski space has this many dimensions since it models spacetime. For 10 points, give the number of dimensions in a tesseract.
This is the only dimension for which the smooth Poincare conjecture has not been resolved and the only dimension for which R to the n has an exotic smooth structure.
four