کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1898392 1533728 2016 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The noncommutative family Atiyah-Patodi-Singer index theorem
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
The noncommutative family Atiyah-Patodi-Singer index theorem
چکیده انگلیسی
In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and we also decompose the Chern character of the index bundle for a fibration with boundary as a pairing of the family Chern-Connes character for a manifold with boundary with the Chern character of an idempotent matrix. We define the family b-Chern-Connes character and then we prove that it is entire and give its variation formula. By this variation formula, we prove another noncommutative family Atiyah-Patodi-Singer index theorem. Thus, we extend the results of Getzler and Wu to the family case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 110, December 2016, Pages 44-59
نویسندگان
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