Enumerating corank 2 complex vector bundles on odd complex projective spaces

Abstract

For $n$ odd, we enumerate rank $n$ complex topological vector bundles on $\mathbb{C}{P}^{n+2}$ with prescribed complex $K$-theory class. The answer exhibits a 24-fold periodicity and is closely related to the enumeration of corank $2$ stably trivial vector bundles.

25 pages, comments welcome!