# Cell-like resolutions of polyhedra by special ones

Dušan Repovš; Arkady Skopenkov

Colloquium Mathematicae (2000)

- Volume: 86, Issue: 2, page 231-237
- ISSN: 0010-1354

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topRepovš, Dušan, and Skopenkov, Arkady. "Cell-like resolutions of polyhedra by special ones." Colloquium Mathematicae 86.2 (2000): 231-237. <http://eudml.org/doc/210852>.

@article{Repovš2000,

abstract = {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.},

author = {Repovš, Dušan, Skopenkov, Arkady},

journal = {Colloquium Mathematicae},

keywords = {banana and pineapple trick; cell-like resolution; Whitehead conjecture; special polyhedron; fake surface; resolutions of polyhedra; Whitehead's asphericity question; special 2-polyhedron; Whitehead's asphericity conjecture},

language = {eng},

number = {2},

pages = {231-237},

title = {Cell-like resolutions of polyhedra by special ones},

url = {http://eudml.org/doc/210852},

volume = {86},

year = {2000},

}

TY - JOUR

AU - Repovš, Dušan

AU - Skopenkov, Arkady

TI - Cell-like resolutions of polyhedra by special ones

JO - Colloquium Mathematicae

PY - 2000

VL - 86

IS - 2

SP - 231

EP - 237

AB - 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.

LA - eng

KW - banana and pineapple trick; cell-like resolution; Whitehead conjecture; special polyhedron; fake surface; resolutions of polyhedra; Whitehead's asphericity question; special 2-polyhedron; Whitehead's asphericity conjecture

UR - http://eudml.org/doc/210852

ER -

## References

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