Exotic diffeomorphisms on a contractible 4-manifold surviving two stabilizations

Abstract

We develop a $\mathrm{Pin}(2)\times {\mathbb{Z}}_2$-equivariant refinement of the lattice homotopy type for computing equivariant Seiberg--Witten Floer homotopy types. As an application, we construct a relatively exotic diffeomorphism on a compact contractible 4-manifold that survives two stabilizations.

131 pages, 1 figures; comments welcome!; minor typos corrected, cleveref problem fixed