| ID | 66005 |
| FullText URL | |
| Author |
Maruyama, Takashi
Department of Engineering, Stanford University
Seto, Tatsuki
General Education and Research Center, Meiji Pharmaceutical University
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| Abstract | In this paper, we generalize the Cantor function to 2-dimensional cubes and construct a cyclic 2-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the 2-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of 2-forms on the torus by using a combinatorial Fredholm module.
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| Keywords | Fredholm module
Cantor dust
cyclic cocycle
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| Note | Mathematics Subject Classification. Primary 46L87; Secondary 28A80.
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| Published Date | 2024-01
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| Publication Title |
Mathematical Journal of Okayama University
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| Volume | volume66
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| Issue | issue1
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| Publisher | Department of Mathematics, Faculty of Science, Okayama University
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| Start Page | 115
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| End Page | 124
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| ISSN | 0030-1566
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| NCID | AA00723502
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| Content Type |
Journal Article
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| language |
English
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| Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University
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| File Version | publisher
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| Refereed |
True
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| Submission Path | mjou/vol66/iss1/8
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