The conjecture is now known to be valid for aspherical manifolds of dimensions greater than four whose fundamental groups contain nilpotent subgroups of finite index (Farrell-Hsiang); earlier work verified the conjecture for free Abelian and poly- fundamental groups.
Offsetsrf Failure On Complex Polysurface Download Citation CopyRequest full-text Download citation Copy link Link copied Request full-text Download citation Copy link Link copied To read the full-text of this research, you can request a copy directly from the authors.Citations (3) References (41) Abstract We study closed topological 2n-dimensional manifolds M with poly-surface fundamental groups.We prove that if M is simple homotopy equivalent to the total space E of a Y-bundle over a closed aspherical surface, where Y is a closed aspherical n-manifold, then M is s-cobordant to E.
Offsetsrf Failure On Complex Polysurface Free Abelian AndThis extends a well-known 4-dimensional result of Hillman in 14 to higher dimensions. Discover the worlds research 17 million members 135 million publications 700k research projects Join for free No full-text available To read the full-text of this research, you can request a copy directly from the authors. By a result of J. Hillman Hil91, Lemma 6 for closed, aspherical surface bundles over surfaces, condition (iii) is satisfied. Indeed, the Mayer-Vietoris argument extends to compact, aspherical surfaces with boundary: each circle C j in the connected-decomposition of the aspherical surface b i F 1 F r generates an indivisible element in the free fundamental group of the many-punctured torus or Klein bottle F k, hence each inclusion 1 (C j ) 1 (F k ) of fundamental groups is square-root closed (see CHS06, Thm. On fibering and splitting of 5-manifolds over the circle Article Jan 2008 TOPOL APPL Qayum Khan Our main result is a generalization of Cappells 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For example, these maps may have homotopy fibers which are in the class of finite connected sums of certain geometric 4-manifolds. Offsetsrf Failure On Complex Polysurface Mod 2 HomologyMost of these homotopy fibers have non-vanishing second mod 2 homology and have fundamental groups of exponential growth, which are not known to be tractable by Freedman--Quinn topological surgery. Indeed, our key technique is topological cobordism, which may not be the trace of surgeries. Indeed, in both cases, the Mayer-Vietoris argument extends to fiber bundles where the surfaces are aspherical, compact, and connected, which are possibly nonorientable and with non-empty boundary (see CHS06, Thm. On smoothable surgery for 4-manifolds Article Mar 2007 Algebr Geomet Topology Qayum Khan Under certain homological hypotheses on a compact 4-manifold, we prove exactness of the topological surgery sequence at the stably smoothable normal invariants. The main examples are the class of finite connected sums of 4-manifolds with certain product geometries. Most of these compact manifolds have non-vanishing second mod 2 homology and have fundamental groups of exponential growth, which are not known to be tractable by Freedman-Quinn topological surgery. Necessarily, the -construction of certain non-smoothable homotopy equivalences requires surgery on topologically embedded 2-spheres and is not attacked here by transversality and cobordism. View Show abstract Special classes of closed four-manifolds Article Full-text available Jan 2001 Alberto Cavicchioli Friedrich Hegenbarth Duan D. Repov Dedicated to the memory of our dear friend Marco Reni Summary. In this paper we present several results and state some open problems on the classification of topological and geometric structures of closed connected oriented (smooth) fourmanifolds. ![]() The results, some of them due to the authors and their collaborators, are ob-tained by using methods and techniques from algebraic and dif-ferential topology, and homological algebra. View Show abstract Four-manifolds with surface fundamental groups Article Full-text available Jan 1997 Alberto Cavicchioli Friedrich Hegenbarth We study the homotopy type of closed connected topological 4- manifolds whose fundamental group is that of an aspherical surface F.T hen we use surgery theory to show that these manifolds are s-cobordant to connected sums of simply-connected manifolds with an S2-bundle over F. View Show abstract A History and Survey of the Novikov Conjecture Article Full-text available Steven C. Ferry Andrew Ranicki Jonathan Rosenberg View Structure Sets Vanish for Certain Bundles over Seifert Manifolds Article Full-text available Feb 1984 T AM MATH SOC Christopher Stark Connected manifolds whose higher homotopy groups vanish are called aspherical. It is known that such a manifold M is determined up to homotopy type by its fundamental group, and the following conjecture is attributed to A. Borel: Conjecture: A closed aspherical manifold is determined up to homeomorphism by its fundamental group.
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