%0 Generic
%A Gaisendrees, Florian Justus
%D 2012
%F heidok:13571
%K Schwache Faserungen , Doldfaserungen , Schnittraumhomologieweak fibrations , Dold fibrations , intersection space homology
%R 10.11588/heidok.00013571
%T Fiberwise Homology Truncation
%U https://archiv.ub.uni-heidelberg.de/volltextserver/13571/
%X Banagl defines a spatial version of intersection homology. A key step is fiberwise homology truncation of the link bundle of a pseudomanifold. The difficulty of extending said results to more general link bundles is informed by two factors: firstly, the type of fiber (which is also the link of the pseudomanifold), and secondly, the base space of the bundle (which is the singular set of the pseudomanifold). We extend the methods of Banagl to link bundles of two types: (1) Fibers CW-complexes with (amongst other conditions) evenly graded homology and base space a sphere. (2) Using a fiber admitting truncation only in selected degrees and base space such that the bundle is glued from two trivial bundles. Different methods are required in each setting. In the first setting, truncation of the fiberwise gluing homeomorphisms yields only homotopy equivalences. Hence homotopy theory is necessary to build a truncated bundle with the right properties. In the second case, this difficulty is not encountered, and no homotopy theory is necessary. Here, we use sheaf theory. In both cases we require the link bundle to be glued from trivial bundles by means of cellular homeomorphisms. Generalized Poincaré duality is shown for pseudomanifolds with each type of link bundle.