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thesis.pdf (614.51 KB)
ETD Abstract Container
Abstract Header
Modular curvature for toric noncommutative manifolds
Author Info
Liu, Yang
ORCID® Identifier
http://orcid.org/0000-0003-0757-2258
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1440121460
Abstract Details
Year and Degree
2015, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
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.
Committee
Henri Moscovici (Advisor)
Ovidiu Costin (Committee Member)
Andrzej Derdzinski (Committee Member)
W. James Waldman (Committee Member)
Pages
137 p.
Subject Headings
Mathematics
Keywords
modular curvature, pseudo differential calculus, noncommutative manifolds
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Citations
Liu, Y. (2015).
Modular curvature for toric noncommutative manifolds
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1440121460
APA Style (7th edition)
Liu, Yang.
Modular curvature for toric noncommutative manifolds.
2015. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1440121460.
MLA Style (8th edition)
Liu, Yang. "Modular curvature for toric noncommutative manifolds." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1440121460
Chicago Manual of Style (17th edition)
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Document number:
osu1440121460
Download Count:
524
Copyright Info
© 2015, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.