کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661308 | 1344420 | 2007 | 23 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cochain algebra on manifolds and convergence under refinement
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold and prove they converge to their differential-geometric analogues as the triangulation becomes small. The first such result is for a cochain cup product converging to the wedge product on differential forms. Moreover, we show any extension of this product to a C∞-algebra also converges to the wedge product of forms. For cochains equipped with an inner product, we define a combinatorial star operator and show that for a certain cochain inner product this operator converges to the smooth Hodge star operator.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 9, 1 May 2007, Pages 1898-1920
Journal: Topology and its Applications - Volume 154, Issue 9, 1 May 2007, Pages 1898-1920