TY - JOUR
T1 - Manifolds that fail to be co-dimension 2 fibrators necessarily cover themselves
AU - Im, Young Ho
AU - Kim, Yongkuk
PY - 2003/2
Y1 - 2003/2
N2 - Let N be a closed s-Hopfian n-manifold with residually finite, torsion free π1(N) and finite H1(N). Suppose that either πk(N) is finitely generated for all k ≥ 2,or πk(N) ≅ 0 for 1 < k < n - 1, or n ≤ 4. We show that if N fails to be a co-dimension 2 fibrator, then N cyclically covers itself, up to homotopy type.
AB - Let N be a closed s-Hopfian n-manifold with residually finite, torsion free π1(N) and finite H1(N). Suppose that either πk(N) is finitely generated for all k ≥ 2,or πk(N) ≅ 0 for 1 < k < n - 1, or n ≤ 4. We show that if N fails to be a co-dimension 2 fibrator, then N cyclically covers itself, up to homotopy type.
KW - Approximate fibration
KW - Residually finite group
KW - s-Hopfian manifold
UR - http://www.scopus.com/inward/record.url?scp=0037302122&partnerID=8YFLogxK
U2 - 10.1017/s1446788700003128
DO - 10.1017/s1446788700003128
M3 - Article
AN - SCOPUS:0037302122
SN - 1446-7887
VL - 74
SP - 61
EP - 67
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 1
ER -