اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRelative topological surgery exact sequence and additivity of relative higher rho invariants
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In this paper, we define the relative higher $rho$ invariant for orientation preserving homotopy equivalence between PL manifolds with boundary in $K$-theory of the relative obstruction algebra, i.e. the relative analytic structure group. We also show that the map induced by the relative higher $rho$ invariant is a group homomorphism from the relative topological structure group to the relative analytic structure group. For this purpose, we generalize Weinberger, Xie and Yus definition of the topological structure group in their article Shmuel Weinberger, Zhizhang Xie, and Guoliang Yu. Additivity of higher rho invariants and nonrigidity of topological manifolds. Communications on Pure and Applied Mathematics, to appear. to make the additive structure of the relative topological structure group transparent.
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