کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665557 1633816 2015 59 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Noncommutative geometry and conformal geometry. III. Vafa–Witten inequality and Poincaré duality
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Noncommutative geometry and conformal geometry. III. Vafa–Witten inequality and Poincaré duality
چکیده انگلیسی

This paper is the third part of a series of papers whose aim is to use the framework of twisted spectral triples to study conformal geometry from a noncommutative geometric viewpoint. In this paper we reformulate the inequality of Vafa–Witten [42] in the setting of twisted spectral triples. This involves a notion of Poincaré duality for twisted spectral triples. Our main results have various consequences. In particular, we obtain a version in conformal geometry of the original inequality of Vafa–Witten, in the sense of an explicit control of the Vafa–Witten bound under conformal changes of metrics. This result has several noncommutative manifestations for conformal deformations of ordinary spectral triples, spectral triples associated with conformal weights on noncommutative tori, and spectral triples associated with duals of torsion-free discrete cocompact subgroups satisfying the Baum–Connes conjecture.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 272, 26 February 2015, Pages 761–819
نویسندگان
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