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

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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 $Spin^c(n)$.

• 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.