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My question has been answered in LemmaTheorem 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.

My question has been answered in Lemma 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.

My question has been answered in Theorem 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.

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My questionsquestion has been answered in Lemma 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.

My questions has been answered in Lemma 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.

My question has been answered in Lemma 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.

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Mathematics enthusiast
Mathematics enthusiast
  • 161
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My questions has been answered in Lemma 3.1 in https://arxiv.org/abs/2404.09023

Indeed, $\pi_{D}\left(\left(\Omega^{d+1}X\right)^{\mathbb{Z}_2},c_{x_0}\right)\cong\pi_{D+1}\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2},c_{x_0}\right)$ for any $\mathbb{Z}_2$-space $X$ with $\mathbb{Z}_2$-fixed point $x_0\in X^{\mathbb{Z}_2}$ which gives rise to the long exact sequence of the pair $\left(\Omega^{d}X,\left(\Omega^{d}X\right)^{\mathbb{Z}_2}\right)$. The map $c_{x_0}$ denotes the constant map to $x_0$.