Show simple item record

dc.contributor.authorRanicki, Andrew
dc.coverage.spatial20en
dc.date.accessioned2003-11-18T10:25:36Z
dc.date.available2003-11-18T10:25:36Z
dc.date.issued2001-11-30
dc.identifier.citationhttp://arxiv.org/pdf/math.AT/0111316en
dc.identifier.urihttp://hdl.handle.net/1842/243
dc.description.abstractThe algebraic theory of surgery gives a necessary and suffcient chain level condition for a space with n-dimensional Poincare duality to be homotopy equivalent to an n- dimensional topological manifold. A relative version gives a necessary and suffcient chain level condition for a simple homotopy equivalence of n-dimensional topological manifolds to be homotopic to a homeomorphism. The chain level obstructions come from a chain level interpretation of the fibre of the assembly map in surgery. The assembly map A : Hn(X;L.) -> Ln(Z[Pi 1 | (X)]) is a natural transformation from the generalized homology groups of a space X with coefficients in the 1-connective simply-connected surgery spectrum L. to the non-simply-connected surgery obstruc- tion groups L.(Z[Pi 1 | (X)]). The (Z;X)-category has objects based f.g. free Z-modules with an X-local structure. The assembly maps A are induced by a functor from the (Z;X)-category to the category of based f.g. free Z[Pi 1 | (X)]-modules. The generalized homology groups H.(X;L.) are the cobordism groups of quadratic Poincare complexes over (Z;X). The relative groups S.(X) in the algebraic surgery exact sequence of X ... -> Hn(X;L.) Aen
dc.format.extent204568 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherNotes of lecture given at the Summer School on High-dimensional Manifold Topology, ICTP Trieste, May-June 2001. To appear in Vol. 1 of the Proceedingsen
dc.subjectsurgery exact sequenceen
dc.subjectstructure seten
dc.subjecttotal surgery obstructionen
dc.titleThe structure set of an arbitrary space, the algebraic surgery exact sequence and the total surgery obstructionen
dc.typePreprinten


Files in this item

This item appears in the following Collection(s)

Show simple item record