A Kastler-Kalau-Walze Type Theorem for 7-Dimensional Manifolds with Boundary

Abstract and Applied Analysis

Research Article

Yong Wang²  Jian Wang¹ 

[1] School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China, nenu.edu.cn;School of Science, Tianjin University of Technology and Education, Tianjin 300222, China, tute.edu.cn;School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China, nenu.edu.cn

Others  :  1320071
DOI  :  10.1155/2014/465782

 received in 2014-06-27, accepted in 2014-08-19,  发布年份 2014

【 摘 要 】

We give a brute-force proof of the Kastler-Kalau-Walze type theorem for 7-dimensional manifolds with boundary.

【 授权许可】

CC BY   
Copyright © 2014 Jian Wang and Yong Wang. 2014

【 参考文献 】

• [1]V. Guillemin. (1985). A new proof of Weyl's formula on the asymptotic distribution of eigenvalues. Advances in Mathematics.55(2):131-160. DOI: 10.1016/0001-8708(85)90018-0.
• [2]M. Wodzicki. (1995). local invariants of spectral asymmetry. Inventiones Mathematicae.75(1):143-178. DOI: 10.1016/0001-8708(85)90018-0.
• [3]M. Adler. (1978/79). On a trace functional for formal pseudo differential operators and the symplectic structure of the Korteweg-de\thinspace Vries type equations. Inventiones Mathematicae.50(3):219-248. DOI: 10.1016/0001-8708(85)90018-0.
• [4]A. Connes. Quantized calculus and applications. :15-36. DOI: 10.1016/0001-8708(85)90018-0.
• [5]A. Connes. (1988). The action functinal in Noncommutative geometry. Communications in Mathematical Physics.117:673-683. DOI: 10.1016/0001-8708(85)90018-0.
• [6]D. Kastler. (1995). The Dirac operator and gravitation. Communications in Mathematical Physics.166(3):633-643. DOI: 10.1016/0001-8708(85)90018-0.
• [7]W. Kalau, M. Walze. (1995). Gravity, non-commutative geometry and the Wodzicki residue. Journal of Geometry and Physics.16(4):327-344. DOI: 10.1016/0001-8708(85)90018-0.
• [8]T. Ackermann. (1996). A note on the Wodzicki residue. Journal of Geometry and Physics.20(4):404-406. DOI: 10.1016/0001-8708(85)90018-0.
• [9]B. V. Fedosov, F. Golse, E. Leichtnam, E. Schrohe. et al.(1996). The noncommutative residue for manifolds with boundary. Journal of Functional Analysis.142(1):1-31. DOI: 10.1016/0001-8708(85)90018-0.
• [10]E. Schrohe. (1999). Noncommutative residue, Dixmier's trace, and heat trace expansions on manifolds with boundary. Contemporary Mathematics.242:161-186. DOI: 10.1016/0001-8708(85)90018-0.
• [11]Y. Wang. (2006). Differential forms and the Wodzicki residue for manifolds with boundary. Journal of Geometry and Physics.56(5):731-753. DOI: 10.1016/0001-8708(85)90018-0.
• [12]S. W. Hawking. (1979). General Relativity. An Einstein Centenary Survey. DOI: 10.1016/0001-8708(85)90018-0.
• [13]Y. Wang. (2007). Gravity and the noncommutative residue for manifolds with boundary. Letters in Mathematical Physics.80(1):37-56. DOI: 10.1016/0001-8708(85)90018-0.
• [14]Y. Wang. (2010). Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary. Communications in Theoretical Physics.54(1):38-42. DOI: 10.1016/0001-8708(85)90018-0.
• [15]R. Ponge. (2008). Noncommutative Geometry and lower dimensional volumes in Riemannian geometry. Letters in Mathematical Physics.83:1-19. DOI: 10.1016/0001-8708(85)90018-0.
• [16]J. Wang, Y. Wang. The Kastler-Kalau-Walze type theorem for 6-dimensional manifolds with boundary. . DOI: 10.1016/0001-8708(85)90018-0.
• [17]Y. Wang. (2014). A Kastler-KALau-Walze type theorem and the spectral action for perturbations of Dirac operators on manifolds with boundary. Abstract and Applied Analysis.2014-13. DOI: 10.1016/0001-8708(85)90018-0.
• [18]J. Wang, Y. Wang. (2013). Noncommutative residue and sub-Dirac operators for foliations. Journal of Mathematical Physics.54(1)-35. DOI: 10.1016/0001-8708(85)90018-0.
• [19]F. Dobarro, B. Ünal. (2005). Curvature of multiply warped products. Journal of Geometry and Physics.55(1):75-106. DOI: 10.1016/0001-8708(85)90018-0.
• [20]W. Zhang. (1989). Local Index Theorem of Atiyah-Singer for Families of Dirac Operators.1369. DOI: 10.1016/0001-8708(85)90018-0.
• [21]Y. Wang. (2014). Multiply warped products with a semisymmetric metric connection. Abstract and Applied Analysis.2014-12. DOI: 10.1016/0001-8708(85)90018-0.