کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8255395 1533705 2018 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Index pairing with Alexander-Spanier cocycles
ترجمه فارسی عنوان
فهرست جفت شدن با تک سلول های اسکندر-اسپانیور
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
چکیده انگلیسی
We give a uniform construction of the higher indices of elliptic operators associated to Alexander-Spanier cocycles of either parity in terms of a pairing à la Connes between theK-theory and the cyclic cohomology of the algebra of complete symbols of pseudodifferential operators, implemented by means of a relative form of the Chern character in cyclic homology. While the formula for the lowest index of an elliptic operator D on a closed manifold M (which coincides with its Fredholm index) reproduces the Atiyah-Singer index theorem, our formula for the highest index of D (associated to a volume cocycle) yields an extension to arbitrary manifolds of any dimension of the Helton-Howe formula for the trace of multicommutators of classical Toeplitz operators on odd-dimensional spheres. In fact, the totality of higher analytic indices for an elliptic operator D amount to a representation of the Connes-Chern character of the K-homology cycle determined by D in terms of expressions which extrapolate the Helton-Howe formula below the dimension of M.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 133, November 2018, Pages 195-209
نویسندگان
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