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- Title
On the cohomology of the classifying spaces of projective unitary groups.
- Authors
Gu, Xing
- Abstract
Let BPU n be the classifying space of PU n , the projective unitary group of order n , for n > 1. We use a Serre spectral sequence to determine the ring structure of H ∗ ( BPU n ; ℤ) up to degree 1 0 , as well as a family of distinguished elements of H 2 p + 2 ( BPU n ; ℤ) , for each prime divisor p of n. We also study the primitive elements of H ∗ ( BU n ; ℤ) as a comodule over H ∗ (K (ℤ , 2) ; ℤ) , where the comodule structure is given by an action of K (ℤ , 2) ≃ BS 1 on BU n corresponding to the action of taking the tensor product of a complex line bundle and an n -dimensional complex vector bundle.
- Subjects
UNITARY groups; PROJECTIVE spaces; BIVECTORS; TENSOR products; SPECTRAL element method; PRODUCT lines; VECTOR bundles
- Publication
Journal of Topology & Analysis, 2021, Vol 13, Issue 2, p535
- ISSN
1793-5253
- Publication type
Article
- DOI
10.1142/S1793525320500211