Smooth involutions and splitting invariants revisited
type: Item
instance of: scholarly article
title: Smooth involutions and splitting invariants revisited
zbMATH Open document ID: 1025.57037
DOI: 10.1016/S0166-8641(02)00143-8
author: Himadri Kumar Mukerjee
published in: Topology and its Applications
publication date: 2003-05-27T00:00:00Z
review text: 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 \( 4\).
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 57R40
zbMATH DE Number: 1917827
zbMATH Keywords: generalized Kervaire invariant
zbMATH Keywords: surgery obstruction
reviewed by: Daniel H. Gottlieb
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1917827