The cohomology and K-theory of the projective unitary groups PU(n)

Abstract

The projective unitary group PU(n) is the group of holomorphic isometries on the complex projective space of dimension n-1. It is essential to the pure Yang-Mills gauge theory, and to the twisted K-theory. Based on the arithmetic and combinatorial properties of the prime factorization of the integer n, we construct the integral cohomology and topological K-theory of the group PU(n), using generators fashioned from the Weyl invariants of the unitary group U(n). Applications to the homotopy and representation theory of the group PU(n) are also discussed.Comment: 23 page