TY - JOUR
T1 - On 2-dimensional Nonaspherical Cell-like Peano Continua
T2 - A Simplified Approach
AU - Eda, Katsuya
AU - Karimov, Umed H.
AU - Repovš, Dušan
PY - 2013/2
Y1 - 2013/2
N2 - We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.
AB - We construct a functor AC(-, -) from the category of path connected spaces X with a base point x to the category of simply connected spaces. The following are the main results of the paper: (i) If X is a Peano continuum then AC(X, x) is a cell-like Peano continuum; (ii) If X is n-dimensional then AC(X, x) is (n + 1)-dimensional; and (iii) For a path connected space X, π1(X, x) is trivial if and only if π2(AC(X, x)) is trivial. As a corollary, AC(S1, x) is a 2-dimensional nonaspherical cell-like Peano continuum.
KW - Alternating cone
KW - asphericity
KW - cell-like space
KW - Noncontractible compactum
KW - Peano continuum
KW - Snake cone
KW - Topologist sine curve
KW - trivial shape
KW - weak homotopy equivalence
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U2 - 10.1007/s00009-011-0165-1
DO - 10.1007/s00009-011-0165-1
M3 - Article
AN - SCOPUS:84873993598
SN - 1660-5446
VL - 10
SP - 519
EP - 528
JO - Mediterranean Journal of Mathematics
JF - Mediterranean Journal of Mathematics
IS - 1
ER -