Summary
The index of a family of a family of Dirac operators is aK-Theory element in the parameter space. Sullivan'sℤ/k-manifolds are used to detect this index completely. For the first Chern class this gives a topological interpretation of Witten's global anomaly. The relationship with the geometry of the index bundle is considered.
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To my teacher Isadore M. Singer
The author is partially supported by an NSF Postdoctoral Research Fellowship
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Freed, D.S. ℤ/k-manifolds and families of Dirac operators. Invent Math 92, 243–254 (1988). https://doi.org/10.1007/BF01404453
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DOI: https://doi.org/10.1007/BF01404453