algebraic topology – application of higher algebra and higher category theory to the study of (stable) homotopy theory
Special and general types
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
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Variants
differential cohomology
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The Adams operations on complex topological K-theory are compatible with the Chern character map to rational cohomology in that the effect of on the Chern character image in degree is multiplication by .
(Adams-like operations on rational cohomology)
For a topological space, with rational cohomology in even degrees denoted
define graded linear maps
for by taking their restriction to degree to act by multiplication with :
(Adams operations compatible with the Chern character)
For a topological space with a finite CW-complex-mathematical structure, the Chern character on the complex topological K-theory of intertwines the Adams operations on K-theory with the Adams-like operations on rational cohomology from Def. , for , in that the following diagram commutes:
(Adams 62, Thm. 5.1. (vi), review in Karoubi 78, Chapter V, Theorem 3.27, Maakestad 06, Thm. 4.9)
Use the exponentional-formula for the Chern character with the splitting principle.
The original statement:
Textbook accounts:
Review and exposition:
Last revised on January 7, 2021 at 13:42:04. See the history of this page for a list of all contributions to it.