Balanced subdivisions and flips on surfaces
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- by Satoshi Murai and Yusuke Suzuki PDF
- Proc. Amer. Math. Soc. 146 (2018), 939-951 Request permission
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.References
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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
- MR Author ID: 800440
- 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
- MR Author ID: 663921
- Email: y-suzuki@math.sc.niigata-u.ac.jp
- 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
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 939-951
- MSC (2010): Primary 05C10; Secondary 57Q15, 52B70
- DOI: https://doi.org/10.1090/proc/13775
- MathSciNet review: 3750208