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Modular curvature for toric noncommutative manifolds
Liu, Yang

2015, Doctor of Philosophy, Ohio State University, Mathematics.
In this paper, we extend recent results on the modular geometry on noncommuta- tive two tori to a larger class of noncommutative manifolds: toric noncommutative manifolds. We first develop a pseudo differential calculus which is suitable for spectral geometry on toric noncommutative manifolds. As a main application, we derive a general expression for the modular curvature with respect to a conformal change of metric on toric noncommutative manifolds. By specializing our results to the noncommutative two and four tori, we recovered the modular curvature functions found in the previous works. An important technical aspect of the computation is that it is is free of computer assistance.
Henri Moscovici (Advisor)
Ovidiu Costin (Committee Member)
Andrzej Derdzinski (Committee Member)
W. James Waldman (Committee Member)
137 p.

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Liu, Y. (2015). Modular curvature for toric noncommutative manifolds. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Liu, Yang. "Modular curvature for toric noncommutative manifolds." Electronic Thesis or Dissertation. Ohio State University, 2015. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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Liu, Yang "Modular curvature for toric noncommutative manifolds." Electronic Thesis or Dissertation. Ohio State University, 2015. https://etd.ohiolink.edu/

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