Main Mathematical Achievement
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