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Difference between revisions of "User:Artemisfowl3rd"

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Test:
 
  
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\begin{tikzcd}
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$$
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A & B \\
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\begin{array}{lcr}  
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C & D
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{i _ {1}} \mathop \cdot \limits  &\mathop \rightarrow \limits ^ {u _ {1}}  &\mathop \cdot \limits {i _ {2}}  \\
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\arrow[""{name=0, anchor=center, inner sep=0}, "f"', from=1-1, to=2-1]
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{} _ {u _ {3}}  \searrow  &{} &\swarrow _ {u _ {2}}  \\
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\arrow[""{name=1, anchor=center, inner sep=0}, "g", from=1-2, to=2-2]
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{}  &\mathop \cdot \limits _ {i _ {3}}  &{} \\  
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\arrow["e", shorten <=6pt, shorten >=6pt, from=0, to=1]
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\end{array}   $$
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\end{tikzcd}
 
  
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\[
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$$  \begin{array}{rcl} 
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\begin{tikzcd}
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i _ {1} \mathop \cdot \limits  &\mathop \rightarrow \limits ^ {u _ {1}}  &\mathop \cdot \limits i _ {2}  \\
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A & B \\
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\scriptsize {u _ {4}} \downarrow  &{}  &\downarrow \scriptsize {u _ {2}}  \\ 
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C & D
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i _ {4} \mathop \cdot \limits  &\mathop \rightarrow \limits _ {u _ {3}}  &\mathop \cdot \limits i _ {3}  \\
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\arrow[""{name=0, anchor=center, inner sep=0}, "f"', from=1-1, to=2-1]
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\end{array} 
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\arrow[""{name=1, anchor=center, inner sep=0}, "g", from=1-2, to=2-2]
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$$
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\arrow["e", shorten <=6pt, shorten >=6pt, from=0, to=1]
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\end{tikzcd}
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$$
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\]
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\begin{array}{rcl}  
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A &{} & B \\
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\scriptsize{f}\Big\downarrow & \xrightarrow{\ \ e\ \ } & \Big\downarrow \scriptsize{g} \\  
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C &{} & D
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\end{array}$$
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$$
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\begin{array}{ccc}
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H^*(W(G,K)) & \xrightarrow[\cong]{\ \ w\ \ } & H^*(EG/K, \mathbf{R}) \\
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\cong \Big\downarrow& & \Big\downarrow \cong\\
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I(K) & \xrightarrow[\cong]{\ \ w\ \ } & H^*(BK, \mathbf{R})
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\end{array}
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$$

Latest revision as of 06:39, 15 February 2024

$$ \begin{array}{lcr} {i _ {1}} \mathop \cdot \limits &\mathop \rightarrow \limits ^ {u _ {1}} &\mathop \cdot \limits {i _ {2}} \\ {} _ {u _ {3}} \searrow &{} &\swarrow _ {u _ {2}} \\ {} &\mathop \cdot \limits _ {i _ {3}} &{} \\ \end{array} $$

$$ \begin{array}{rcl} i _ {1} \mathop \cdot \limits &\mathop \rightarrow \limits ^ {u _ {1}} &\mathop \cdot \limits i _ {2} \\ \scriptsize {u _ {4}} \downarrow &{} &\downarrow \scriptsize {u _ {2}} \\ i _ {4} \mathop \cdot \limits &\mathop \rightarrow \limits _ {u _ {3}} &\mathop \cdot \limits i _ {3} \\ \end{array} $$

$$ \begin{array}{rcl} A &{} & B \\ \scriptsize{f}\Big\downarrow & \xrightarrow{\ \ e\ \ } & \Big\downarrow \scriptsize{g} \\ C &{} & D \end{array}$$

$$ \begin{array}{ccc} H^*(W(G,K)) & \xrightarrow[\cong]{\ \ w\ \ } & H^*(EG/K, \mathbf{R}) \\ \cong \Big\downarrow& & \Big\downarrow \cong\\ I(K) & \xrightarrow[\cong]{\ \ w\ \ } & H^*(BK, \mathbf{R}) \end{array} $$

How to Cite This Entry:
Artemisfowl3rd. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Artemisfowl3rd&oldid=55441
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