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تسجيل مستخدم جديدThe index of families of projective operators
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تأليف
Alexandre Baldare
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Following [44], we introduce the notion of families of projective operators on fibrations equipped with an Azumaya bundle $mathcal{A}$. We define and compute the index of such families using the cohomological index formula from [7]. More precisely, a family of projective operators $A$ can be pulled back in a family $tilde{A}$ of $SU(N)$-transversally elliptic operators on the $PU(N)$-principal bundle of trivialisations of $mathcal{A}$. Through the distributional index of $tilde{A}$, we can define an index for the family $A$ of projective operators and using the cohomological index formula from [7], we obtain an explicit cohomological index formula. Let $1 to Gamma to tilde{G} to G to 1$ be a central extension by an abelian finite group. As a preliminary result, we compute the index of families of $tilde{G}$-transversally elliptic operators on a $G$-principal bundle $P$.
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