nLab
BSU(n)
Contents
Contents
Idea
is the classifying space for the special unitary group .
Definition
Definition
is the limit of the sequence of canonical inclusions of complex orientable Grassmannians :
As the complex
orientable Grassmannian can be written as a homogenous space by
the group structure carries over to .
Smallest classifying space
Since is the trivial group, the classifying space is the trivial topological space. Since , once has
Cohomology
Theorem
The cohomology ring of with coefficients in the ring of integers is generated by the Chern classes and given by
(Hatcher 02, Example 4D.7.)
Colimit
The canonical inclusions yield canonical inclusions of their respective classifying spaces. The colimit is denoted as
and indeed the classifying space for .
References
Created on March 14, 2024 at 15:50:56.
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