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Mar 29, 2019 at 17:01 comment added André Henriques Correct. They can only be defined because TL is orientable (a non-orientable real line bundle does not have a notion of real power).
Mar 29, 2019 at 2:15 comment added David Roberts What are the real tensor powers? Are they the line bundles whose transition functions are real powers of the usual ones for $TL$?
Mar 29, 2019 at 0:29 history answered André Henriques CC BY-SA 4.0