Relative Differential K-theory

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Abstract (2. Language): 
Let p : Y — X be a smooth map between two smooth compact manifolds. We define the relative differential K-theory group K*(p) and show that it fits into a six-term exact sequence. We define K*(p,R/Z), the K-theory of p with R/Z coefficients. It turns out that K*(p,R/Z) is isomorphic to the group of homomorphisms from the relative K-homology of p [8] to R/Z up to a degree-shift by one.



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