Abstract
We give a transparent description of the one-fold smooth suspension of Fintushel-Stern's exotic involution on the 4-sphere. Moreover we prove that any two involutions of the 4-sphere are stably (i.e., after one-fold suspension) smoothly conjugated if and only if the corresponding quotient spaces (real homotopy projective spaces) are stably diffeomorphic. We use the Atiyah-Patodi-Singer eta-invariant to detect smooth structures on homotopy projective spaces and prove that any homotopy projective space is detected in this way in dimensions 5 and 6.
Citation
Wieslaw J. Oledzki. "Exotic involutions of low-dimensional spheres and the eta-invariant." Tohoku Math. J. (2) 52 (2) 173 - 198, 2000. https://doi.org/10.2748/tmj/1178224606
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