The generators of the K-groups of the sphere

Hermann Schulz-Baldes, Tom Stoiber

Published 2024-03-27Version 1

This note presents an elementary iterative construction of the generators for the complex $K$-groups $K_i(C(\SM^d))$ of the $d$-dimensional spheres. These generators are explicitly given as the restrictions of Dirac or Weyl Hamiltonians to the unit sphere. Connections to solid state physics are briefly elaborated on.