Operators on symmetric polynomials and applications in computing the cohomology of $BPU_n$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916495753216000 |
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| author | Fan, Feifei |
| author_facet | Fan, Feifei |
| contents | This paper studies the integral cohomology ring of the classifying space $BPU_n$ of the projective unitary group $PU_n$. By calculating a Serre spectral sequence, we determine the ring stucture of $H^*(BPU_n;\mathbb{Z})$ in dimensions $\leq 11$. For any odd prime $p$, we also determine the $p$-primary subgroups of $H^i(BPU_n;\mathbb{Z})$ in the range $i\leq 2p+13$ for $i$ odd and $i\leq 4p+8$ for $i$ even. The main technique used in the calculation is applying the theory of Young diagrams and Schur polynomials to certain linear operators on symmetric polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11691 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operators on symmetric polynomials and applications in computing the cohomology of $BPU_n$ Fan, Feifei Algebraic Topology This paper studies the integral cohomology ring of the classifying space $BPU_n$ of the projective unitary group $PU_n$. By calculating a Serre spectral sequence, we determine the ring stucture of $H^*(BPU_n;\mathbb{Z})$ in dimensions $\leq 11$. For any odd prime $p$, we also determine the $p$-primary subgroups of $H^i(BPU_n;\mathbb{Z})$ in the range $i\leq 2p+13$ for $i$ odd and $i\leq 4p+8$ for $i$ even. The main technique used in the calculation is applying the theory of Young diagrams and Schur polynomials to certain linear operators on symmetric polynomials. |
| title | Operators on symmetric polynomials and applications in computing the cohomology of $BPU_n$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2410.11691 |