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John N.
John N.
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I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the $2-$dimensional torus $T^2$. In particular I am interested on the $K_0-$group. I have read that the generators of the group $K_0(C(T^2))$ are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.

I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the $2-$dimensional torus $T^2$. In particular I am interested on the $K_0-$group. I have read that the generators are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.

I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the $2-$dimensional torus $T^2$. In particular I am interested on the $K_0-$group. I have read that the generators of the group $K_0(C(T^2))$ are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.

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John N.
John N.
  • 743
  • 3
  • 13

K-theory for the $C^*-$algebra of the continuous functions on the torus$2-$torus and the Bott projection

I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the $2-$dimensional torus $T^2$. In particular I am interested on the $K_0-$group. I have read that the generators are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.

K-theory for the $C^*-$algebra of the continuous functions on the torus and the Bott projection

I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the torus. In particular I am interested on the $K_0-$group. I have read that the generators are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.

K-theory for the $C^*-$algebra of the continuous functions on the $2-$torus and the Bott projection

I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the $2-$dimensional torus $T^2$. In particular I am interested on the $K_0-$group. I have read that the generators are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.

Source Link
John N.
John N.
  • 743
  • 3
  • 13

K-theory for the $C^*-$algebra of the continuous functions on the torus and the Bott projection

I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the torus. In particular I am interested on the $K_0-$group. I have read that the generators are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.