Celebratio Mathematica — Rourke

My collaboration with Colin Rourke

Works connected to Dennis P. Sullivan

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C. P. Rourke and D. P. Sullivan: “On the Kervaire obstruction,” Ann. of Math. (2) 94 (1971), pp. 397–413. MR 305416 Zbl 0227.57012 article

The purpose of this paper is to give a geometrical definition, based on immersion theory, of this obstruction, the Kervaire obstruction, and to prove a product formula which gives the obstruction for \( f \times g \) in terms of invariants of \( f \) and \( g \). The definition and formula apply when \( M \) is non-simply connected and \( n \) is any even integer but in this case the obstruction is just part of the surgery obstruction. We also interpret the product formula in terms of the classifying space \( G/PL \) for \( PL \) normal maps. It implies the existence of primitive “Kervaire” classes in the \( \mathbb{Z}_2 \)-cohomology of \( G/PL \) which induce the obstruction. We give formulae due to Brumfiel and Wall relating the various classes.

A. A. Ranicki, A. J. Casson, D. P. Sullivan, M. A. Armstrong, C. P. Rourke, and G. E. Cooke: The Hauptvermutung book: A collection of papers of the topology of manifolds. \( K \)-Monographs in Mathematics 1. Kluwer Academic Publishers (Dordrecht), 1996. MR 1434100 Zbl 0853.00012 book

Andrew J. Casson	Related
Dennis P. Sullivan	Related
Mark Anthony Armstrong	Related
George E. Cooke	Related
Andrew A. Ranicki	Related	Volume