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Non-trivial K-theory groups and non-trivial cobordism groups can lead toglobal symmetries which are conjectured to be absent in quantum gravity.Inspired by open-closed string duality, we propose a correspondence between thetwo groups, which can be considered as the physical manifestation of ageneralisation of the classic Conner--Floyd isomorphism. The picture isexemplified by the relations between KO-groups and Spin-cobordisms and betweenK-groups and Spin$^c$-cobordisms. Global symmetries related by such isomorphismare eventually gauged. By combining K-theory and cobordism, we recover thentadpole cancellation conditions in type I string theory and F-theory from abottom-up perspective.

Open-Closed Correspondence of K-theory and Cobordism