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We show that unstable D-branes play the role of "D-sphalerons" in string theory. Their existence implies that the configuration space of type-II string theory has a complicated homotopy structure, similar to that of an infinite grassmannian. In particular, the configuration space of type-IIA (-IIB) string theory on R 10 has non-trivial homotopy groups π k for all k even (odd).1 Such unstable D-branes (in particular, the spacetime-filling D9-branes) are indeed crucial in the systematic classification of D-brane charges in type-IIA theory and its relation to K −1 (X) groups of spacetime [4].2 In this paper, we focus on type-IIA and type-IIB string theory in R 10 , making only occasional comments about orientifolds and compactifications.

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