On the Cohomology of the Classifying Spaces of Projective Unitary Groups
| Autor: | Gu, Xing |
|---|---|
| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S1793525320500211 |
| Popis: | Let $\mathbf{B}PU_{n}$ be the classifying space of $PU_n$, the projective unitary group of order $n$, for $n>1$. We use the Serre spectral sequence associated to a fiber sequence $\mathbf{B}U_n\rightarrow\mathbf{B}PU_n\rightarrow K(\mathbb{Z},3)$ to determine the ring structure of $H^{*}(\mathbf{B}PU_{n}; \mathbb{Z})$ up to degree $10$, as well as a family of distinguished elements of $H^{2p+2}(\mathbf{B}PU_{n}; \mathbb{Z})$, for each prime divisor $p$ of $n$. We also study the primitive elements of $H^*(\mathbf{B}U_n;\mathbb{Z})$ as a comodule over $H^*(K(\mathbb{Z},2);\mathbb{Z})$, where the comodule structure is given by an action of $K(\mathbb{Z},2)\simeq\mathbf{B}S^1$ on $BU_n$ corresponding to the action of taking the tensor product of a complex line bundle and an $n$ dimensional complex vector bundle. Comment: 43 pages, 3 figures. Published version plus an appendix. Accepted by the Journal of Topology and Analysis |
| Databáze: | arXiv |
| Externí odkaz: |
|