Homeomorphic spherical manifolds that are not diffeomorphic
Answers
Answered by
0
It is known that spheres of dimension less than 66 have a unique smooth structure but the 77-sphere admits 2828distinct smooth structures and generally the nn-sphere admits more than one smooth structure for n>7n>7.
I do not have an exact reference available but i think you can find these in lots of places like for example Kosinski's book, 1993, on Differential manifolds. I am not sure if all these admit compatible complex structures though.
Regarding the symplectic structures, maybe you can find something of interest in Uniqueness of symplectic structures, where the author discusses uniqueness questions of symplectic forms on compact manifolds without boundary.
I do not have an exact reference available but i think you can find these in lots of places like for example Kosinski's book, 1993, on Differential manifolds. I am not sure if all these admit compatible complex structures though.
Regarding the symplectic structures, maybe you can find something of interest in Uniqueness of symplectic structures, where the author discusses uniqueness questions of symplectic forms on compact manifolds without boundary.
Similar questions