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A coloring invariant of 3-manifolds derived from their flow-spines and virtual knot diagrams

Published online by Cambridge University Press:  02 May 2023

Ippei Ishii ,
Takuji Nakamura  and
Toshio Saito Open the ORCID record for Toshio Saito [Opens in a new window]
Ippei Ishii
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku, Yokohama 223-8522, Japan
Takuji Nakamura
Affiliation:
Faculty of Education, University of Yamanashi, 4-4-37 Takeda, Kofu, Yamanashi 400-8510, Japan e-mail: takunakamura@yamanashi.ac.jp
Toshio Saito*
Affiliation:
Department of Mathematics, Joetsu University of Education, 1 Yamayashiki, Joetsu 943-8512, Japan
*
e-mail: toshio@juen.ac.jp
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Abstract

For a closed, connected, and oriented 3-manifold with a non-singular flow, we construct its virtual knot diagram via a “flow-spine” of the manifold. Then, we introduce a coloring invariant of 3-manifolds through their virtual knot diagrams, and classify some 3-manifolds by using the invariant.

Keywords

Coloring invariant3-manifoldflow-spinevirtual knot diagram
Type
Article
Information
Canadian Journal of Mathematics , Volume 76 , Issue 3 , June 2024 , pp. 984 - 1004
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

This work was supported by JSPS KAKENHI (Grant Nos. JP20K03621 and JP21K03244).

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