TY - JOUR
T1 - The mapping class groups of reducible heegaard splittings of genus two
AU - Cho, Sangbum
AU - Koda, Yuya
N1 - 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 Science, ICT, and Future Planning (NRF-2015R1A1A1A05001071), and by the Ministry of Education (NRF-201800000001768). The second author was supported by JSPS KAKENHI Grant Numbers 15H03620, 17K05254, 17H06463, and JST CREST Grant Number JPMJCR17J4.
Funding Information:
Received by the editors February 21, 2017, and, in revised form, July 12, 2017, and August 21, 2017. 2010 Mathematics Subject Classification. Primary 57N10, 57M60. 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 Science, ICT, and Future Planning (NRF-2015R1A1A1A05001071), and by the Ministry of Education (NRF-201800000001768). The second author was supported by JSPS KAKENHI Grant Numbers 15H03620, 17K05254, 17H06463, and JST CREST Grant Number JPMJCR17J4.
Publisher Copyright:
© 2018 American Mathematical Society.
PY - 2019
Y1 - 2019
N2 - A 3-manifold which admits a genus-2 reducible Heegaard splitting is one of the 3-sphere, S 2 × S 1 , lens spaces and their connected sums. For each of those manifolds except most lens spaces, the mapping class group of the genus-2 splitting was shown to be finitely presented. In this work, we study the remaining generic lens spaces and show that the mapping class group of the genus-2 Heegaard splitting is finitely presented for any lens space by giving its explicit presentation. As an application, we show that the fundamental groups of the spaces of the genus-2 Heegaard splittings of lens spaces are all finitely presented.
AB - A 3-manifold which admits a genus-2 reducible Heegaard splitting is one of the 3-sphere, S 2 × S 1 , lens spaces and their connected sums. For each of those manifolds except most lens spaces, the mapping class group of the genus-2 splitting was shown to be finitely presented. In this work, we study the remaining generic lens spaces and show that the mapping class group of the genus-2 Heegaard splitting is finitely presented for any lens space by giving its explicit presentation. As an application, we show that the fundamental groups of the spaces of the genus-2 Heegaard splittings of lens spaces are all finitely presented.
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U2 - 10.1090/tran/7375
DO - 10.1090/tran/7375
M3 - Article
AN - SCOPUS:85042494599
SN - 0002-9947
VL - 371
SP - 2473
EP - 2502
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 4
ER -