For cofibrant suppose there is a universal cocycle
that encodes the integral cohomology of .
this may be resolved to a morphism in
Using the path ∞-groupoid this induces a morphism in cohomology
The term on the left is just -cohomology . The term on the right is in (abelian) nonabelian deRham cohomology. Since the -part of the cocycle only contributes on constant paths, and since there the cocycle is forced to be trivial, this is equivalent to the same expression with replaced by just . This way in summary we obtain a morphism
from -cohomology to real cohomology. This is the nonabelian Chern character for us.
Last revised on January 22, 2010 at 13:26:45.
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