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2000 | 86 | 2 | 231-237
Tytuł artykułu

Cell-like resolutions of polyhedra by special ones

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Suppose that P is a finite 2-polyhedron. We prove that there exists a PL surjective map f:Q → P from a fake surface Q with preimages of f either points or arcs or 2-disks. This yields a reduction of the Whitehead asphericity conjecture (which asserts that every subpolyhedron of an aspherical 2-polyhedron is also aspherical) to the case of fake surfaces. Moreover, if the set of points of P having a neighbourhood homeomorphic to the 2-disk is a disjoint union of open 2-disks, and every point of P has an arbitrarily small 2-dimensional neighbourhood, then we may additionally conclude that Q is a special 2-polyhedron.
Rocznik
Tom
86
Numer
2
Strony
231-237
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-06
poprawiono
2000-01-21
Twórcy
  • Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001
  • Department of Mathematics, Kolmogorov College, Kremenchugskaya, 11, Moscow, Russia 121357
Bibliografia
  • [Da86] R. J. Daverman, Decomposition of Manifolds, Academic Press, New York, 1986.
  • [HMS93] C. Hog-Angeloni, W. Metzler and A. J. Sieradski (eds.), Two-Dimensional Homotopy and Combinatorial Group Theory, London Math. Soc. Lecture Note Ser. 197, Cambridge Univ. Press, Cambridge, 1993.
  • [La77] R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), 336-552.
  • [Ma73] S. V. Matveev, Special skeletons of PL manifolds, Mat. Sb. 92 (1973), 287-293 (in Russian).
  • [MR88] W. J. R. Mitchell and D. Repovš, The topology of cell-like mappings, Rend. Sem. Fac. Sci. Univ. Cagliari Suppl. 58 (1988), 265-300.
  • [RS72] C. P. Rourke and B. J. Sanderson, Introduction to Piecewise-Linear Topology, Ergeb. Math. Grenzgeb. 69, Springer, Berlin, 1972.
  • [Sa] K. Salikhov, Non-existence of special resolutions of 2-polyhedra by special ones, preprint.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv86i2p231bwm
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