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Reza Rezazadegan
Reza Rezazadegan
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My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. II've learned one way to prove this can be provesis using the fact that the group $Br_n$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).

My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. I learned this can be proves using the fact that the group $Br_n$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).

My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. I've learned one way to prove this is using the fact that the group $Br_n$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).

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Reza Rezazadegan
Reza Rezazadegan
  • 803
  • 6
  • 14

My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. I learned this can be proves using the fact that the group $Br_m$$Br_n$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).

My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. I learned this can be proves using the fact that the group $Br_m$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).

My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. I learned this can be proves using the fact that the group $Br_n$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).

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Reza Rezazadegan
Reza Rezazadegan
  • 803
  • 6
  • 14

2-cells in the configuration space

My overarching question is why in the Artin presentation of the (geometrically defined) braid group there are no more than two relations. I learned this can be proves using the fact that the group $Br_m$ is the $\pi_1$ of configuration space $Conf_n=(\mathbb{C}^n\backslash \{z_i=z_j, i\neq j\})/S_n$ together with the fact that when computing the $\pi_1$ of a CW complex you can restrict your attention to its 2-skeleton.

Now I'm wondering if there is an explicit description of a cell decomposition for the configuration space (in particular of the 1- and 2-cells in it).