A note on the homotopical characterization of Rn

• Autores: Rafael Ayala Gómez , Antonio Rafael Quintero Toscano
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 43, Fasc. 3, 1992, págs. 191-196
• Idioma: inglés
• Títulos paralelos:
  • Una nota sobre la caracterización homotópica de Rn
• Enlaces
  • Texto completo
• Resumen

  • This note gives conditions which assure that the one-point compactification of an open manifold is a manifold. This result is used to show that the homotopical characterization of $\mathbb{R}^n (n\geq 4)$ can be derived from the Poincaré Conjecture.

• Referencias bibliográficas
  • J.L. Bryant and R.C. Lacher, Resolving zero-dimensional singularities in generalized manifolds, Math. Proc. Camb. Philos. Soc. 83 (1978),...
  • R.J. Daverman, Decompositions of manifolds, Academic Press, 1986.
  • M.W. Davis, Groups generated by reflections and spherical manifold not covered by Euclidean spaces, Ann. Math. 117 (1983), 293–324.
  • J. Dydak, Local $n$-connectivity of quotient spaces and one-point compactifications, Shape Theory and Geometric Topology, Proceedings, Dubrovnik,...
  • M.H. Freedman, The topology of four dimensional manifolds, J. Differential Geometry 17 (1982), 357–453.
  • R. Geoghegan, Topology Methods in Group Theory, Draft. Dept. of Mathematics, SUNY at Binghamton.
  • L. Glaser, Geometrical Combinatorial Topology, II, Van Nostrand, 1972.
  • M.J. Greenberg, Lectures on Algebraic Topology, Benjamin, 1967.
  • R.C. Kirby and L.C. Siebenmann, On the triangulation of manifolds and the Hauptvermutung, Bull. Amer. Math. Soc. 75 (1969), 742–749.
  • E. Luft, On contractible open manifolds, Inv. Math. 4 (1967), 192–201.
  • S. Mardešić and J. Segal, Shape Theory, North-Holland, 1982.
  • W. Massey, Homology and cohomology theory, Marcel Dekker, 1978.
  • M.H.A. Newman, The engulfing theorem for topological manifolds, Ann. of Math. 84 (1966), 555–571.
  • F. Quinn, Ends of maps III: Dimension 4 and 5, J. Differential Geometry 17 (1982), 503–521.
  • D. Repovš, A criterion for compactification of open 3-manifolds, Preprint, Institute of Mathematics, University of Ljubljana, 1992.
  • L.C. Siebenmann, On deleting Euclidean Space homotopically among topological manifolds, Inv. Math. 6 (1968), 245–261.
  • L.C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension greater than five, thesis, Princeton, 1965.
  • S. Smale, Generalized Poincaré’s Conjecture in dimensions greater than four, Ann. of Math. 74 (1961), 391–406.
  • C.T.C. Wall, Open 3-manifolds which are 1-connected at infinity, Quart. J. Math. 16 (1965), 263–268.
  • D.G. Wright, Contractible open manifolds which are not covering spaces, Topology 31 (1992), 281–292.