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تسجيل مستخدم جديدFiniteness of $A_n$-equivalence types of gauge groups
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تأليف
Mitsunobu Tsutaya
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Let $B$ be a finite CW complex and $G$ a compact connected Lie group. We show that the number of gauge groups of principal $G$-bundles over $B$ is finite up to $A_n$-equivalence for $n<infty$. As an example, we give a lower bound of the number of $A_n$-equivalence types of gauge groups of principal $SU(2)$-bundles over $S^4$.
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We construct the homotopy pullback of $A_n$-spaces and show some universal property of it. As the first application, we review the Zabrodskys result which states that for each prime $p$, there is a finite CW complex which admits an $A_{p-1}$-form but
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