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SOME RECENT APPROACHES IN 4–DIMENSIONAL SURGERY THEORY

By et al. Friedrich Hegenbarth

Abstract

It is well-known that an n-dimensional Poincaré complex X n, n ≥ 5, has the homotopy type of a compact topological n–manifold if the total surgery obstruction s(Xn) vanishes. The present paper discusses recent attempts to prove analogous result in dimension 4. We begin by reviewing the necessary algebraic and controlled surgery theory. Next, we discuss the key idea of Quinn’s approach. Finally, we present some cases of special fundamental groups, due to the authors and to Yamasaki

Year: 2005
OAI identifier: oai:CiteSeerX.psu:10.1.1.193.4553
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