TY - JOUR
T1 - Partial euler characteristic, normal generations and the stable D(2) problem
AU - Ji, Feng
AU - Ye, Shengkui
N1 - Publisher Copyright:
© 2018, International Press.
PY - 2018
Y1 - 2018
N2 - We study the interplay amongWall's D(2) problem, the normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex X of cohomological dimension 2 with finite fundamental group, assuming the Wiegold conjecture holds, we prove that X is homotopy equivalent to a finite 2-complex after wedging a copy of sphere S2.
AB - We study the interplay amongWall's D(2) problem, the normal generation conjecture (the Wiegold Conjecture) of perfect groups and Swan's problem on partial Euler characteristic and deficiency of groups. In particular, for a 3-dimensional complex X of cohomological dimension 2 with finite fundamental group, assuming the Wiegold conjecture holds, we prove that X is homotopy equivalent to a finite 2-complex after wedging a copy of sphere S2.
KW - Cohomological dimensions
KW - D(2) problem
KW - Quillen's plus construction
UR - http://www.scopus.com/inward/record.url?scp=85050995623&partnerID=8YFLogxK
U2 - 10.4310/HHA.2018.V20.N2.A6
DO - 10.4310/HHA.2018.V20.N2.A6
M3 - Article
AN - SCOPUS:85050995623
SN - 1532-0073
VL - 20
SP - 105
EP - 114
JO - Homology, Homotopy and Applications
JF - Homology, Homotopy and Applications
IS - 2
ER -