3-sphere two 3-balls. This construction is analogous to a construction of a 2-sphere, performed by gluing the boundaries of a pair of disks. A disk is a 2-ball, and the boundary of a disk is a circle (a 1-sphere). Let a pair of disks be of the same diameter. Superpose them and glue corresponding points on their boundaries. Again one may think of the third dimension as temperature. Likewise, we may inflate the 2-sphere, moving the pair of disks to become the northern and southern hemispheres. After removing a single point from the 2-sphere, what remains is homeomorphic to the Euclidean
Sphere spectrum denoted by formula_1. Sphere spectrum In stable homotopy theory, a branch of mathematics, the sphere spectrum "S" is the initial object in the category of spectra. It is the suspension spectrum of "S", i.e., a set of two points. Explicitly, the "n"th space in the sphere spectrum is the "n"-dimensional sphere "S", and the structure maps from the suspension of "S" to "S" are the canonical homeomorphisms. The "k"-th homotopy group of a sphere spectrum is the "k"-th stable homotopy group of spheres. The localization of the sphere spectrum at a prime number "p" is called the local sphere at