Tohoku Mathematical Journal
2000
June
SECOND SERIES VOL. 52, NO. 2

Tohoku Math. J.
52 (2000), 173-198

Title EXOTIC INVOLUTIONS OF LOW-DIMENSIONAL SPHERES AND THE ETA-INVARIANT

Author Wieslaw J. Oledzki

(Received May 27, 1998, revised October 22, 1999)
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.

1991 Mathematics Subject Classification. Primary 57R55; Secondary 53C10, 53C21, 57R60, 58G10, 58G25.
Key words and phrases. Involutions on spheres, homotopy projective spaces, cobordism, Dirac-type operators, eta-invariant.

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