Balanced subdivisions and flips on surfaces

Murai, Satoshi; Suzuki, Yusuke

doi:10.1090/proc/13775

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.

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