@article{275155f19fb542e0afa90a7a983e194f,
title = "Disk surgery and the primitive disk complexes of the 3-sphere",
abstract = "It is known that the primitive disk complex for a genus-2 Heegaard splitting of the 3-sphere is closed under disk surgery operation. We show that, for a genus-g Heegaard splitting of the 3-sphere with g≥3, the primitive disk complex for the splitting is not weakly closed under disk surgery operation. That is, there exist two primitive disks in one of the handlebodies of the splitting such that any disk surgery on one along the other one yields no primitive disks.",
keywords = "Disk complex, Disk surgery, Heegaard splitting, Primitive disk",
author = "Sangbum Cho and Yuya Koda and Lee, {Jung Hoon}",
note = "Funding Information: The first-named author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-201800000001768 ). The second-named author is supported in part by JSPS KAKENHI Grant Numbers JP15H03620 , JP17K05254 , JP17H06463 , and JST CREST Grant Number JPMJCR17J4 . The third-named author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( 2018R1D1A1A09081849 ). Publisher Copyright: {\textcopyright} 2020 Elsevier B.V.",
year = "2020",
month = mar,
day = "1",
doi = "10.1016/j.topol.2020.107092",
language = "English",
volume = "272",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
}