A Composition Formula for Manifold Structures

Andrew Ranicki

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

The structure set S-TOP (M) of an n-dimensional topological manifold M for n >= 5 has a homotopy invariant functorial abelian group structure, by the algebraic version of the Browder-Novikov-Sullivan-Wall surgery theory. An element (N, f) is an element of S-TOP (M) is an equivalence class of n-dimensional manifolds N with a homotopy equivalence f : N -> M. The composition formula is that (P, fg) = (N, f) + f(*)(P, g) is an element of S-TOP (M) for homotopy equivalences g : P -> N, F : N -> M. The formula is required for a paper of Kreck and Luck

Original languageEnglish
Pages (from-to)701-727
Number of pages27
JournalPure and applied mathematics quarterly
Volume5
Issue number2
Publication statusPublished - Apr 2009

Keywords / Materials (for Non-textual outputs)

  • Topological manifold
  • structure set
  • surgery theory

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