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.
Publié le : 2000-05-14
Classification:
Involutions on spheres,
homotopy projective spaces,
cobordism,
Dirac-type operators,
eta-invariant,
57R55,
57R60,
57S17,
58J28
@article{1178224606,
author = {Oledzki, Wieslaw J.},
title = {Exotic involutions of low-dimensional spheres and the eta-invariant},
journal = {Tohoku Math. J. (2)},
volume = {52},
number = {4},
year = {2000},
pages = { 173-198},
language = {en},
url = {http://dml.mathdoc.fr/item/1178224606}
}
Oledzki, Wieslaw J. Exotic involutions of low-dimensional spheres and the eta-invariant. Tohoku Math. J. (2), Tome 52 (2000) no. 4, pp. 173-198. http://gdmltest.u-ga.fr/item/1178224606/