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Minimal Finite Models

Part of the Lecture Notes in Mathematics book series (LNM,volume 2032)

Abstract

In Sect. 3.3 we proved that in general, if K is a finite simplicial complex, there is no finite space with the homotopy type of |K|. However, by Theorem 2.4.12 any compact polyhedron is weak homotopy equivalent to a finite space. In this chapter we will study finite models of polyhedra in this sense and we will describe the minimal finite models of some well-known (Hausdorff) spaces, i.e. weak homotopy equivalent finite spaces of minimum cardinality. The main results of this chapter appear in [7].

Keywords

  • Fundamental Group
  • Simplicial Complex
  • Homotopy Type
  • Homotopy Group
  • Algebraic Topology

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2011 Springer-Verlag Berlin Heidelberg

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Barmak, J.A. (2011). Minimal Finite Models. In: Algebraic Topology of Finite Topological Spaces and Applications. Lecture Notes in Mathematics(), vol 2032. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22003-6_3

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