کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425665 1633838 2014 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A relative higher index theorem, diffeomorphisms and positive scalar curvature
ترجمه فارسی عنوان
قضیه شاخص نسبت نسبی بالاتر، اختلاف مورفیسم و ​​انحنای اسکالر مثبت
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی

We prove a general relative higher index theorem for complete manifolds with positive scalar curvature towards infinity. We apply this theorem to study Riemannian metrics of positive scalar curvature on manifolds. For every two metrics of positive scalar curvature on a closed manifold and a Galois cover of the manifold, we define a secondary higher index class. Non-vanishing of this higher index class is an obstruction for the two metrics to be in the same connected component of the space of metrics of positive scalar curvature. In the special case where one metric is induced from the other by a diffeomorphism of the manifold, we obtain a formula for computing this higher index class. In particular, it follows that the higher index class lies in the image of the Baum-Connes assembly map.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 250, 15 January 2014, Pages 35-73
نویسندگان
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