偶数维带边流形上的一类Kastler-Kalau-Walze类型定理

doi:10.3969/j.issn.1000-5641.2021.03.004

华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (3): 23-33.doi: 10.3969/j.issn.1000-5641.2021.03.004

偶数维带边流形上的一类Kastler-Kalau-Walze类型定理

包开花^1,*(), 孙爱慧², 夏令远³

1. 内蒙古民族大学数理学院, 内蒙古通辽　028000
2. 吉林师范大学数学学院, 吉林四平　136000
3. 东北师范大学数学与统计学院, 长春　130024

收稿日期:2020-02-04 出版日期:2021-05-25 发布日期:2021-05-26
通讯作者: 包开花 E-mail:baokh505@nenu.edu.cn
基金资助:
国家自然科学基金(11901322); 内蒙古自治区自然科学基金(2018LHO1004)

Kastler-Kalau-Walze type theorems for an even dimensional manifold with boundary

Kaihua BAO^1,*(), Aihui SUN², Lingyuan XIA³

1. College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao Inner Mongolia　028000, China
2. College of Mathematics, Jilin Normal University, Siping Jilin　136000, China
3. School of Mathematics and Statistics, Northeast Normal University, Changchun　130024, China

Received:2020-02-04 Online:2021-05-25 Published:2021-05-26
Contact: Kaihua BAO E-mail:baokh505@nenu.edu.cn

摘要/Abstract

摘要：

在任意偶数维带边Spin流形上建立了一类关于带挠率的Dirac算子的Kastler-Kalau-Walze类型定理, 为相应流形上的Einstein-Hilbert作用给出了简单的算子理论解释.

关键词: 带挠率的Dirac算子, 非交换留数, 低维体积, 偶数维带边流形

Abstract:

In this paper, we establish a Kastler-Kalau-Walze type theorem for an even dimensional manifold with boundary about Dirac operators with torsion; in addition, we provide a simple theoretical explanation to the Einstein-Hilbert action for any even dimensional manifold with boundary.

Key words: Dirac operators with torsion, noncommutative residue, lower-dimensional volumes, even dimensional manifold with boundary

中图分类号:

O186

包开花, 孙爱慧, 夏令远. 偶数维带边流形上的一类Kastler-Kalau-Walze类型定理[J]. 华东师范大学学报（自然科学版）, 2021, 2021(3): 23-33.

Kaihua BAO, Aihui SUN, Lingyuan XIA. Kastler-Kalau-Walze type theorems for an even dimensional manifold with boundary[J]. Journal of East China Normal University(Natural Science), 2021, 2021(3): 23-33.

参考文献 20

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偶数维带边流形上的一类Kastler-Kalau-Walze类型定理

Kastler-Kalau-Walze type theorems for an even dimensional manifold with boundary

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