Researches Supported by Kakenhi
Masaharu Morimoto

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1. April 2018 -- Marchi 2023: Study of group actions on manifolds by means of pseudo inverse limit systems of equivariant framed maps
   
   
   • We proved that the 6-dimensional sphere has effective one-fixed-point smooth G-actions for G = A_5, A_5 x Z_2 and S_6, and
     tha 7-dimensional sphere has effective one-fixed-point smooth G-actions for G = A_5, A_5 x Z_2 and SL(2, 5) x Z_r with (r, 30) = 1.
   
   
   • Let N(G) be the set of integers n such that there is an effective one-fixzed-point smooth G-action on the n-dimensional sphere.
     We determined N(G) for G = A_5 and S_5.
     In addition we proved that G = A_5 x Z_2 has effective one-fixed-point smooth actions on the n-dimensional spheres for the integers n which is greater than 5 and not equal to 9.
   
   

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