String${}^{\mathbf{c}}$ Structures and Modular Invariants

Abstract

In this paper, we study some algebraic topology aspects of String${}^c$ structures, more precisely, from the perspective of Whitehead tower and the perspective of the loop group of $Spi{n}^c(n)$. We also extend the generalized Witten genera constructed for the first time in \cite{CHZ11} to correspond to String${}^c$ structures of various levels and give vanishing results for them.

41 pages; to appear in the Transactions of the American Mathematical Society