Letters in Mathematical Physics

, Volume 80, Issue 1, pp 37–56 | Cite as

Gravity and the Noncommutative Residue for Manifolds with Boundary

  • Yong Wang


We prove a Kastler–Kalau–Walze type theorem for the Dirac operator and the signature operator for 3,4-dimensional manifolds with boundary. As a corollary, we give two kinds of operator-theoretic explanations of the gravitational action in the case of 4-dimensional manifolds with flat boundary.

Mathematics Subject Classification (2000)

58G20 53A30 46L87 


noncommutative residue for manifolds with boundary gravitational action for manifolds with boundary 


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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNortheast Normal UniversityChangchunChina
  2. 2.Center of Mathematical SciencesZhejiang UniversityHangzhouChina

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