Chern-Weil Homomorphism

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I would like you to help me prove the theorem related to Chern-Weil Homomorphism



Theorem (Rigidity Property). Let $A$ be a locally free $mathfrakg$-da. Any two $mathfrakg$-ds homomorphisms $c_0,c_1:W_mathfrakgrightarrow A$ that agree on the unit of $W_mathfrakg$ are $mathfrakg$-homotopic.



Corollary. Let $A$ be a locally free $mathfrakg$-da and $c:W_mathfrakgrightarrow A$ be a $mathfrakg$-ds homomorphism taking the unit of $W_mathfrakg$ to the unit of $A$. Then induced map in basic cohomology $$left ( Smathfrakg^ast right )_invrightarrow left ( Hmathfrakg^ast right )_inv$$



is an algebra homomorphism, independent of the choice of $c$.



Thanks for your help.




homology-cohomology




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  • Missing: your work. From the question asking form: "Provide details. Share your research."
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up vote
-3
down vote

favorite












I would like you to help me prove the theorem related to Chern-Weil Homomorphism



Theorem (Rigidity Property). Let $A$ be a locally free $mathfrakg$-da. Any two $mathfrakg$-ds homomorphisms $c_0,c_1:W_mathfrakgrightarrow A$ that agree on the unit of $W_mathfrakg$ are $mathfrakg$-homotopic.



Corollary. Let $A$ be a locally free $mathfrakg$-da and $c:W_mathfrakgrightarrow A$ be a $mathfrakg$-ds homomorphism taking the unit of $W_mathfrakg$ to the unit of $A$. Then induced map in basic cohomology $$left ( Smathfrakg^ast right )_invrightarrow left ( Hmathfrakg^ast right )_inv$$



is an algebra homomorphism, independent of the choice of $c$.



Thanks for your help.




homology-cohomology




share|cite|improve this question



















  • Missing: your work. From the question asking form: "Provide details. Share your research."
    – Eric Towers
    Jul 27 at 23:09












up vote
-3
down vote

favorite









up vote
-3
down vote

favorite











I would like you to help me prove the theorem related to Chern-Weil Homomorphism



Theorem (Rigidity Property). Let $A$ be a locally free $mathfrakg$-da. Any two $mathfrakg$-ds homomorphisms $c_0,c_1:W_mathfrakgrightarrow A$ that agree on the unit of $W_mathfrakg$ are $mathfrakg$-homotopic.



Corollary. Let $A$ be a locally free $mathfrakg$-da and $c:W_mathfrakgrightarrow A$ be a $mathfrakg$-ds homomorphism taking the unit of $W_mathfrakg$ to the unit of $A$. Then induced map in basic cohomology $$left ( Smathfrakg^ast right )_invrightarrow left ( Hmathfrakg^ast right )_inv$$



is an algebra homomorphism, independent of the choice of $c$.



Thanks for your help.




homology-cohomology




share|cite|improve this question











I would like you to help me prove the theorem related to Chern-Weil Homomorphism



Theorem (Rigidity Property). Let $A$ be a locally free $mathfrakg$-da. Any two $mathfrakg$-ds homomorphisms $c_0,c_1:W_mathfrakgrightarrow A$ that agree on the unit of $W_mathfrakg$ are $mathfrakg$-homotopic.



Corollary. Let $A$ be a locally free $mathfrakg$-da and $c:W_mathfrakgrightarrow A$ be a $mathfrakg$-ds homomorphism taking the unit of $W_mathfrakg$ to the unit of $A$. Then induced map in basic cohomology $$left ( Smathfrakg^ast right )_invrightarrow left ( Hmathfrakg^ast right )_inv$$



is an algebra homomorphism, independent of the choice of $c$.



Thanks for your help.





homology-cohomology





share|cite|improve this question










share|cite|improve this question




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asked Jul 27 at 23:06









Victor Huuanca Sullca

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  • Missing: your work. From the question asking form: "Provide details. Share your research."
    – Eric Towers
    Jul 27 at 23:09
















  • Missing: your work. From the question asking form: "Provide details. Share your research."
    – Eric Towers
    Jul 27 at 23:09















Missing: your work. From the question asking form: "Provide details. Share your research."
– Eric Towers
Jul 27 at 23:09




Missing: your work. From the question asking form: "Provide details. Share your research."
– Eric Towers
Jul 27 at 23:09















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