Cell-like resolutions of polyhedra by special ones

• Autorzy: Dušan Repovš , Arkady Skopenkov
• 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.

Słowa kluczowe

EN

banana and pineapple trick; cell-like resolution; Whitehead conjecture; special polyhedron; fake surface

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 86
• Numer: 2
• Strony: 231-237

Daty

wydano

2000

otrzymano

1999-12-06

poprawiono

2000-01-21

Twórcy

autor

Dušan Repovš

• Institute of Mathematics, Physics and Mechanics, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001

autor

Arkady Skopenkov

• Department of Mathematics, Kolmogorov College, Kremenchugskaya, 11, Moscow, Russia 121357

Bibliografia

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