Splitting of the Family Index

@inproceedings{Dai2004SplittingOT,
  title={Splitting of the Family Index},
  author={Xianzhe Dai and Weiping Zhang},
  year={2004}
}
We establish a general splitting formula for index bundles of families of Dirac type operators. Among the applications, our result provides a positive answer to a question of Bismut and Cheeger [BC2]. 
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