Smooth involutions and splitting invariants revisited
The author strengthens results of \textit{William Browder} [Trans. Am. Math. Soc. 178, 193-225 (1978; Zbl 0261.57014)]. In that paper, Browder generalized the Kervaire invariant and calculated it subject to a technical condition. With this at hand, he was able to study involutions on smooth homotopy spheres. The author eliminates the technical hypothesis from Browder's theorem by showing that the hypothesis always holds for any double covering. The author exploits this advance with applications to splitting invariants along products of real projective spaces, and to embedding of real Milnor manifolds in projective spaces of dimension congruent to \(1\) mod \( 4\).
scientific article; zbMATH DE number 1917827
scientific article