On Samelson products in $SU(n)$-and $Sp(n)$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929741691355136 |
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| author | Mohammadi, Sajjad |
| author_facet | Mohammadi, Sajjad |
| contents | Let $a$ and $b$ be two positive integers such that $a, b < n$. We denote the inclusion $Σ\mathbb{C}P^a\rightarrow SU(n)$ by $\varepsilon_{a,n}$. Also, let $m$ and $n$ be two positive integers such that $m < n$. This article has two parts. In the first part, we will study the order of the Samelson product $\langle \varepsilon_{a,n}, \varepsilon_{b,n}\rangle$ where $a+b=n+k$, for $k \geq 0$. Also, we will give two applications. In the second part, we will study the order of the Samelson product $S^{4m-1}\wedge Q_{n-m+1}\rightarrow Sp(n)$, where $Q_{n-m+1}$ is the symplectic quasi-projective space of rank $n-m+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13340 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Samelson products in $SU(n)$-and $Sp(n)$ Mohammadi, Sajjad Algebraic Topology 55Q15, 55P10 A.0 Let $a$ and $b$ be two positive integers such that $a, b < n$. We denote the inclusion $Σ\mathbb{C}P^a\rightarrow SU(n)$ by $\varepsilon_{a,n}$. Also, let $m$ and $n$ be two positive integers such that $m < n$. This article has two parts. In the first part, we will study the order of the Samelson product $\langle \varepsilon_{a,n}, \varepsilon_{b,n}\rangle$ where $a+b=n+k$, for $k \geq 0$. Also, we will give two applications. In the second part, we will study the order of the Samelson product $S^{4m-1}\wedge Q_{n-m+1}\rightarrow Sp(n)$, where $Q_{n-m+1}$ is the symplectic quasi-projective space of rank $n-m+1$. |
| title | On Samelson products in $SU(n)$-and $Sp(n)$ |
| topic | Algebraic Topology 55Q15, 55P10 A.0 |
| url | https://arxiv.org/abs/2307.13340 |