Main Mathematical Achievement

Masaharu Morimoto

- He solved Laitinen-Traczyk's Problem. That is, he proved that the alternating group of degree 5 smoothly acts on the 6-dimensional sphere with exactly one fixed point.
- He solved Oliver-Petrie's Problem. Namely, he proved with E. Laitinen that a finite group G can smoothly act on a standard sphere of some dimension with exactly one fixed point if and only if G never admits a normal series P =< H =< G such that P and G/H are groups of prime power order and H/P is cyclic.
- He proved with A. Bak that a standard sphere has a smooth action on it with exactly one fixed point from the alternating group of degree 5 if the dimension of the sphere is equal to or greater than 6.
- He found the first counterexample to Laitinen's conjecture. That is, for G = Aut(A_6), the Smith set Sm(G) is trivial although a_G is equal to 2, where a_G denote the number of real conjugacy classes of g in G such that the order of g is not a prime power order.
- He constructed various equivariant surgery theories, e.g. equivariant surgery theory on compact manifolds with middle dimensional singular sets, and provided new surgery obstruction groups relevant to quadratic form parameters and symmetric form parameters.
- He found an additively closed subset A(G) of the primary Smith set Sm(G)_P in RO(G) such that A(G) occupies a large portion of Sm(G)_P. (In general, Sm(G)_P is not additively closed in RO(G). This set A(G) is useful to determine the primary Smith set Sm(G)_P.)

Home Page of M. Morimoto