Abstract
In this paper, we study some algebraic topology aspects of String c ^c structures, more precisely, from the perspective of Whitehead tower and the perspective of the loop group of S p i n c ( n ) Spin^c(n) . We also extend the generalized Witten genera constructed for the first time by Chen et al. [J. Differential Geom. 88 (2011), pp. 1â40] to correspond to String c ^c structures of various levels and give vanishing results for them.
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