Determine the inertia group of complex projective space

Determine the inertia group of complex projective space \(\mathbb{C}P^m\) in arbitrary dimensions, extending beyond the currently available low-dimensional computations.

Background

The paper studies the inertia group $I(\mathbb{C}P^m)$, consisting of exotic spheres whose connected sum with $\mathbb{C}P^m$ is diffeomorphic to $\mathbb{C}P^m$. It relates the concordance inertia group to the kernel of the map induced by the quotient $q:\mathbb{C}P^m\to S^{2m}$, and uses $EO$-theory to detect families of exotic spheres lying outside the inertia group.

Although the paper establishes nontrivial lower-bound information by exhibiting exotic spheres outside $I(\mathbb{C}P^m)$ in several infinite families of dimensions, it does not determine the full inertia group. The authors explicitly characterize the general computation as largely unresolved, with prior explicit results confined to low dimensions.