algebraic topology – application of higher algebra and higher category theory to the study of (stable) homotopy theory
group cohomology, nonabelian group cohomology, Lie group cohomology
Hochschild cohomology, cyclic cohomology?
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
For a complex vector bundle of complex rank , the highest degree Chern class that may generally be non-vanishing is . This is hence often called the top Chern class of the vector bundle.
The top Chern class of a complex vector bundle equals the Euler class of the underlying real vector bundle :
(e.g. Bott-Tu 82 (20.10.6))
The top Chern class of a complex vector bundle equals the pullback of any Thom class on along the zero-section:
(e.g. Bott-Tu 82, Prop. 12.4)
This relation to Thom classes generalizes to Conner-Floyd-Chern classes in complex oriented Whitehead-generalized cohomology. See at universal complex orientation on MU.
For more references see at Chern class and at characteristic class.
Created on January 26, 2021 at 08:52:54. See the history of this page for a list of all contributions to it.