Celebratio Mathematica

C. P. Rourke and B. J. Sanderson: “An embedding without a normal microbundle,” Invent. Math. 3 (1967), pp. 293–299. MR 222904 Zbl 0168.44602 article

C. P. Rourke and B. J. Sanderson: “Block bundles, I,” Ann. of Math. (2) 87 (1968), pp. 1–28. MR 226645 Zbl 0215.52204 article

C. P. Rourke and B. J. Sanderson: “Block bundles, II: Transversality,” Ann. of Math. (2) 87 (1968), pp. 256–278. MR 226646 Zbl 0215.52301 article

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.

C. P. Rourke and B. J. Sanderson: Introduction to piecewise-linear topology. Ergeb. Math. Grenzgeb. 69. Springer, 1972. MR 350744 Zbl 0254.57010 book

The first five chapters of this book form an introductory course in piecewise-linear topology in which no assumptions are made other than basic topological notions. This course would be suitable as a second course in topology with a geometric flavour, to follow a first course in point-set topology, and perhaps to be given as a final year undergraduate course. The whole book gives an account of handle theory in a piecewiselinear setting and could be the basis of a first-year postgraduate lecture or reading course. Some results from algebraic topology are needed for handle theory and these are collected in an appendix. In a second appendix are listed the properties of Whitehead torsion which are used in the \( s \)-cobordism theorem. These appendices should enable a reader with only basic knowledge to complete the book. The book is also intended to form an introduction to modern geometric topology as a research subject, a bibliography of research papers being included. We have omitted acknowledgements and references from the main text and have collected these in a set of “historical notes” to be found after the appendices.

S. Buoncristiano, C. P. Rourke, and B. J. Sanderson: A geometric approach to homology theory. London Mathematical Society Lecture Note Series 18. Cambridge University Press; London Mathematical Society (Cambridge; London), 1976. MR 413113 Zbl 0315.55002 book

Sandro Buoncristiano	Related
Brian Joseph Sanderson	Related

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

C. Rourke: The geometry of the universe. Series on Knots and Everything 71. World Scientific Publishing (Hackensack, NJ), 2021. MR 4375354 book

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Colin P. Rourke

Colin Patrick Rourke: a short biography

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