The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary
Abstract
:1. Introduction
2. The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Its Lichnerowicz Formula
- (1)
3. A Kastler–Kalau–Walze-Type Theorem for 4-Dimensional Manifolds with Boundary
- Then, a) , for any , and b) it is the unique continuous trace on .
4. A Kastler–Kalau–Walze-Type Theorem for 6-Dimensional Manifolds with Boundary
- By the composition formula of pseudodifferential operators, we obtain the following equality:
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Wu, T.; Wang, Y. The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary. Mathematics 2024, 12, 3530. https://doi.org/10.3390/math12223530
Wu T, Wang Y. The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary. Mathematics. 2024; 12(22):3530. https://doi.org/10.3390/math12223530
Chicago/Turabian StyleWu, Tong, and Yong Wang. 2024. "The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary" Mathematics 12, no. 22: 3530. https://doi.org/10.3390/math12223530
APA StyleWu, T., & Wang, Y. (2024). The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary. Mathematics, 12(22), 3530. https://doi.org/10.3390/math12223530