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Tim Perutz
Tim Perutz
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About Why must a reducible flat connectionsSU(2)-connection over a homology sphere be trivial?

Let M$M$ be a homology sphere. Suppose P=M*SU(2)$P=M\times SU(2)$ is the trivial SU(2)$SU(2)$ principal bundle. Let R Let $R$ be all reducible connections on P$P$. Here A$A$ in R$R$ is reducible if the gauge transformation group acting on A$A$ has nontrivial stable subgroup. I want to see that the only flat connection in R$R$ is the Productproduct connection. Thanks.

About flat connections

Let M be a homology sphere. Suppose P=M*SU(2) is the trivial SU(2) principal bundle. Let R be all reducible connections on P. Here A in R is reducible if the gauge transformation group acting on A has nontrivial stable subgroup. I want to see that the only flat connection in R is the Product connection. Thanks.

Why must a reducible flat SU(2)-connection over a homology sphere be trivial?

Let $M$ be a homology sphere. Suppose $P=M\times SU(2)$ is the trivial $SU(2)$ principal bundle. Let $R$ be all reducible connections on $P$. Here $A$ in $R$ is reducible if the gauge transformation group acting on $A$ has nontrivial stable subgroup. I want to see that the only flat connection in $R$ is the product connection.

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Xuanting Cai
Xuanting Cai
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About flat connections

Let M be a homology sphere. Suppose P=M*SU(2) is the trivial SU(2) principal bundle. Let R be all reducible connections on P. Here A in R is reducible if the gauge transformation group acting on A has nontrivial stable subgroup. I want to see that the only flat connection in R is the Product connection. Thanks.