Open Access
January 2021 The Region Smoothing Swap Game
Allison Henrich, Inga Johnson, Jonah Ostroff
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Osaka J. Math. 58(1): 171-187 (January 2021).


We introduce a topological combinatorial game called the Region Smoothing Swap Game. The game is played on a game board derived from the connected shadow of a link diagram on a (possibly non-orientable) surface by smoothing at crossings. Moves in the game are performed on regions of the diagram and can switch the direction of certain crossings' smoothings. The players' goals relate to the connectedness of the diagram produced by game play.


The authors would like to thank the Simons Foundation (#426566, Allison Henrich) for their support of this research.


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Allison Henrich. Inga Johnson. Jonah Ostroff. "The Region Smoothing Swap Game." Osaka J. Math. 58 (1) 171 - 187, January 2021.


Received: 4 October 2019; Published: January 2021
First available in Project Euclid: 9 May 2021

Primary: 57K10 , 91A05 , 91A43 , 91A46

Rights: Copyright © 2021 Osaka University and Osaka City University, Departments of Mathematics

Vol.58 • No. 1 • January 2021
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