K-Theory and the Hopf invariant
Papakonstantinou, Anne Janes
Rector, David L.
Master of Arts
The determination of which spheres, Sn, posses the structure of an H-space is an important question in Algebraic Topology. This thesis will discuss a proof of Theorem (Adams): Sn has an H-structure if and only if n = 0, 1, 3 or 7 . One defines an invariant called the Hopf Invariant which allows one to prove Theorem (Adams): There is a map f: S2n-1 -> Sn of Hopf Invariant 1 if and only if n = 1, 2, 4, or 8. The proof of this theorem uses the K-theory methods of Adams and Atiyah.