Geodesic
Cell-like resolutions of polyhedra by special ones
Colloquium Mathematicum, Tome 86 (2000) no. 2, pp. 231-237 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm-86-2-231-237
Keywords: banana and pineapple trick, cell-like resolution, Whitehead conjecture, special polyhedron, fake surface 
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Dušan Repovš; Arkady Skopenkov. Cell-like resolutions of polyhedra by special ones. Colloquium Mathematicum, Tome 86 (2000) no. 2, pp. 231-237. doi: 10.4064/cm-86-2-231-237

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