ID | 66005 |
FullText URL | |
Author |
Maruyama, Takashi
Department of Engineering, Stanford University
Seto, Tatsuki
General Education and Research Center, Meiji Pharmaceutical University
|
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.
|
Keywords | Fredholm module
Cantor dust
cyclic cocycle
|
Note | Mathematics Subject Classification. Primary 46L87; Secondary 28A80.
|
Published Date | 2024-01
|
Publication Title |
Mathematical Journal of Okayama University
|
Volume | volume66
|
Issue | issue1
|
Publisher | Department of Mathematics, Faculty of Science, Okayama University
|
Start Page | 115
|
End Page | 124
|
ISSN | 0030-1566
|
NCID | AA00723502
|
Content Type |
Journal Article
|
language |
English
|
Copyright Holders | Copyright ©2024 by the Editorial Board of Mathematical Journal of Okayama University
|
File Version | publisher
|
Refereed |
True
|
Submission Path | mjou/vol66/iss1/8
|