A note on the concordance homotopy group of real projective space

Abstract

By means of the mapping torus construction the following theorem is proved Theorem. If r ≡ 3 mod 4 r \equiv 3 \bmod 4 and r ⩾ 7 r \geqslant 7 , and P r {\mathcal {P}_r} is a homotopy P r {P_r} , then there is an isomorphism π 0 Diff + : P r ≅ π 0 Diff + : P r {\pi _0}\;{\operatorname {Diff}^ + }:{\mathcal {P}_r} \cong {\pi _0}\;{\operatorname {Diff}^ + }:{P_r} .