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Balanced subdivisions and flips on surfaces


Authors: Satoshi Murai and Yusuke Suzuki
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 05C10; Secondary 57Q15, 52B70
DOI: https://doi.org/10.1090/proc/13775
Published electronically: October 23, 2017
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Abstract: In this paper, we show that two balanced triangulations of a closed surface are not necessarily connected by a sequence of balanced stellar subdivisions and welds. This answers a question posed by Izmestiev, Klee and Novik. We also show that two balanced triangulations of a closed surface are connected by a sequence of three local operations, which we call the pentagon contraction, the balanced edge subdivision and the balanced edge weld. In addition, we prove that two balanced triangulations of the $ 2$-sphere are connected by a sequence of pentagon contractions and their inverses if none of them are the octahedral sphere.


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Additional Information

Satoshi Murai
Affiliation: Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Suita, Osaka, 565-0871, Japan
Email: s-murai@ist.osaka-u.ac.jp

Yusuke Suzuki
Affiliation: Department of Mathematics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, Niigata, 950-2181, Japan
Email: y-suzuki@math.sc.niigata-u.ac.jp

DOI: https://doi.org/10.1090/proc/13775
Received by editor(s): January 31, 2017
Received by editor(s) in revised form: April 5, 2017, and April 12, 2017
Published electronically: October 23, 2017
Additional Notes: The first author was partially supported by KAKENHI16K05102.
The second author was partially supported by KAKENHI16K05250.
Communicated by: Patricia L. Hersh
Article copyright: © Copyright 2017 American Mathematical Society