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I am interested in knowing about current research in the Topological K-Theory, especially its interactions with String Theory. About one and a half decade back, there were some papers by Physicists (e.g. 1, 2) about relation of Topological K-theory to string theory. Are there any interesting open problems in this area ?

What are the current open problems in Topological K- Theory motivated by String Theory ?

My immediate interest is in Topological K-Theory (and not much in differential K-theory or K-theory of operator algebras or Algebraic K-theory).

Please advise some recent review paper in this area.

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