Cell-like resolutions of polyhedra by special ones

Tom 86 / 2000

Dušan Repovš, Arkady Skopenkov Colloquium Mathematicum 86 (2000), 231-237 DOI: 10.4064/cm-86-2-231-237


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.


  • Dušan Repovš
  • Arkady Skopenkov

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