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 -