TY - JOUR
T1 - Balanced subdivisions and flips on surfaces
AU - Murai, Satoshi
AU - Suzuki, Yusuke
N1 - Publisher Copyright:
© 2017 American Mathematical Society.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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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U2 - 10.1090/proc/13775
DO - 10.1090/proc/13775
M3 - Article
AN - SCOPUS:85041553329
SN - 0002-9939
VL - 146
SP - 939
EP - 951
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -