TY - JOUR
T1 - Extending finite group actions on surfaces over S3
AU - Wang, Chao
AU - Wang, Shicheng
AU - Zhang, Yimu
AU - Zimmermann, Bruno
PY - 2013/10/1
Y1 - 2013/10/1
N2 - Let OEg (resp. CEg and AEg) and resp. OEgo be the maximum order of finite (resp. cyclic and abelian) groups G acting on the closed orientable surfaces σg which extend over (S3, σg) among all embeddings σg→S3 and resp. unknotted embeddings σg→S3.It is known that OEgo≤12(g-1), and we show that 12(g-1) is reached for an unknotted embedding σg→S3 if and only if g=2, 3, 4, 5, 6, 9, 11, 17, 25, 97, 121, 241, 601. Moreover AEg is 2g+2; and CEg is 2g+2 for even g, and 2g-2 for odd g.Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere.
AB - Let OEg (resp. CEg and AEg) and resp. OEgo be the maximum order of finite (resp. cyclic and abelian) groups G acting on the closed orientable surfaces σg which extend over (S3, σg) among all embeddings σg→S3 and resp. unknotted embeddings σg→S3.It is known that OEgo≤12(g-1), and we show that 12(g-1) is reached for an unknotted embedding σg→S3 if and only if g=2, 3, 4, 5, 6, 9, 11, 17, 25, 97, 121, 241, 601. Moreover AEg is 2g+2; and CEg is 2g+2 for even g, and 2g-2 for odd g.Efforts are made to see intuitively how these maximal symmetries are embedded into the symmetries of the 3-sphere.
KW - Extendable action
KW - Finite group action
KW - Maximum order
KW - Symmetry of 3-sphere
KW - Symmetry of surface
UR - https://www.scopus.com/pages/publications/84884587084
U2 - 10.1016/j.topol.2013.08.014
DO - 10.1016/j.topol.2013.08.014
M3 - 文章
AN - SCOPUS:84884587084
SN - 0166-8641
VL - 160
SP - 2088
EP - 2103
JO - Topology and its Applications
JF - Topology and its Applications
IS - 16
ER -