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Differential cohomology theories are sheaves on manifolds

Posted in
Luuk Stehouwer
Wed, 2021-06-16 16:15 - 17:45

Meeting-ID: 994 2805 4844
For passcode contact Christian Kaiser (kaiser@mpim...).


Generalized cohomology theories can be described by spectra. One approach
to differential cohomology theories defines them as 'smooth spectra':
sheaves on manifolds with values in spectra. This abstract categorical
definition allows for a general 'recollement' theorem, which tells one
precisely how to build a differential cohomology theory: you need a
spectrum, certain geometric data and a 'way to mix the two'. It can then be
shown that every such differential cohomology theory fits a certain hexagon
diagram similar to what we have seen in the first talk. We then discuss
examples, in particular recovering Deligne cohomology.

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