Esfera homológica de Poincaré

  1. Alejandro O. Majadas-Moure 1
  1. 1 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

Journal:
TEMat: Divulgación de trabajos de estudiantes de matemáticas

ISSN: 2530-9633

Year of publication: 2023

Issue: 7

Pages: 41-50

Type: Article

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More publications in: TEMat: Divulgación de trabajos de estudiantes de matemáticas

Abstract

From the Poincaré homology sphere it is possible to obtain a natural example of a homology manifold that is not a topological manifold. In general, the Poincaré homology sphere is constructed using geometric arguments related with the dodecahedron. However, we will show another construction using an algebraic point of view.

Bibliographic References

  • BOOTHBY, William M. An introduction to differentiable manifolds and Riemannian geometry. Pure and Applied Mathematics, No. 63. Academic Press [Harcourt Brace Jovanovich, Publishers], NewYork-London, 1975.
  • BOURBAKI, N. Éléments de mathématique. Topologie algébrique. Chapitres 1 à 4. Springer, Heidelberg, 2016. ISBN: 978-3-662-49360-1; 978-3-662-49361-8.
  • DOAN, Aleksander. Easier proof about suspension of a manifold. https://math.stackexchange.com/. 15 de mayo de 2014.
  • HATCHER, Allen. Algebraic topology. Cambridge University Press, Cambridge, 2002. ISBN: 0-521-79160-X; 0-521-79540-0.
  • KIRBY, R. C. y SCHARLEMANN, M. G. “Eight faces of the Poincaré homology3-sphere”. En: Geometrictopology (Proc. Georgia Topology Conf., Athens, Ga., 1977). Academic Press, New York-London, 1979, págs. 113-146.
  • LANG, Serge. Algebra. 2ed. Addison-Wesley Publishing Company, Advanced Book Program, Reading, MA, 1984. ISBN: 978-0-201-05487-3.
  • MUNKRES, James R. Elements of algebraic topology. Addison-Wesley Publishing Company, Menlo Park, CA, 1984. ISBN: 978-0-201-04586-4.
  • PRASOLOV, Viktor V. Elements of combinatorial and differential topology. Vol. 74. Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2006. https://doi.org/10.1090/gsm/074.
  • ROTMAN, Joseph J. An introduction to algebraic topology. Vol. 119. Graduate Texts in Mathematics. Springer-Verlag, New York, 1988. https://doi.org/10.1007/978-1-4612-4576-6.
  • SPANIER, Edwin H. Algebraic topology. McGraw-Hill Book Co., New York-Toronto-London, 1966.
  • THOMASSEN, Carsten. “The Jordan-Schönflies theorem and the classification of surfaces”. En: American Mathematical Monthly 99.2 (1992), págs. 116-130. ISSN: 0002-9890. https://doi.org/10.2307/2324180.
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