All Questions

Let $E=[E^+]-[E^-]$ be an element of the Grothendieck group $K(X)$ of a compact Kahler manifold $X$. Does it exist a way to define more "geometric" structures on $E\in K(X)$ such that a ...

I have heard that there is a proof of non-existence of complex structure on the 4-sphere $S^{4}$ using only the topological K-theory (complex $KU$ and real $KO$). Moreover this argument can not be ...