Report 36/2006: Mini-workshop: The Hauptvermutung for high-dimensional manifolds (August 13th – August 19th, 2006). (English) Zbl 1109.57300

Oberwolfach Rep. 3, No. 3, 2195-2225 (2006).

Abstract: The meeting was devoted to the Kirby-Siebenmann structure theory for high-dimensional topological manifolds and the related disproof of the Hauptvermutung. We found nothing fundamentally wrong with the original work of Kirby and Siebenmann, which is solidly grounded in the literature. Their determination of TOP/PL depends on Kirby’s paper on the Annulus Conjecture and his ‘torus trick’, and the well-known surgery theoretic classification of homotopy tori.
Contributions:

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Arthur Bartels, Topological transversality (p. 2201)

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Allegra E. Berliner and Stacy L. Hoehn, Microbundles (p. 2201)

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William Browder, Topology in the 1960’s: Reminiscences and commentary (p. 2203)

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Diarmuid J. Crowley, Siebenmann’s periodicity mistake (p. 2207)

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James F. Davis, The Product Structure Theorem (p. 2209)

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Ian Hambleton, The classification of homotopy tori (p. 2212)

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Qayum Khan and Tibor Macko, The homotopy type of G/PL and the characteristic variety theorem (p. 2212)

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Andrew Korzeniewski, Milnor’s counter-example to the Hauptvermutung (p. 2215)

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Matthias Kreck, A Proof of Rohlin’s Theorem and the Computation of the Low Dimensional, Spin Bordism Groups (p. 2215)

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Erik Kjær Pedersen, TOP/PL using bounded surgery (p. 2217)

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Ulrich Pennig, Handlebody decompositions of high-dimensional TOP manifolds (p. 2218)

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Frank Quinn, Periodicity and the Hauptvermutung (p. 2218)

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Andrew Ranicki, The manifold Hauptvermutung and the Siebenmann periodicity from the algebraic surgery point of view (p. 2219)

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Michael Weiss, Identifying the algebraic and topological surgery exact sequences (p. 2222)

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Masayuki Yamasaki, A user’s guide to the algebraic theory of surgery (p. 2223)

MSC:

57N15	Topology of the Euclidean \(n\)-space, \(n\)-manifolds (\(4 \leq n \leq \infty\)) (MSC2010)
57Q25	Comparison of PL-structures: classification, Hauptvermutung
00B05	Collections of abstracts of lectures