TY - JOUR
T1 - Fundamental groups, homology equivalences and one-sided h-cobordisms
AU - Su, Yang
AU - Ye, Sheng Kui
N1 - Publisher Copyright:
© 2015, Science China Press and Springer-Verlag Berlin Heidelberg.
PY - 2015/9/17
Y1 - 2015/9/17
N2 - We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes (manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen’s plus construction with Whitehead torsions.
AB - We give a necessary and sufficient condition for the fundamental group homomorphism of a map between CW-complexes (manifolds) to induce partial homology equivalences. As applications, we obtain characterizations of fundamental groups of homology spheres and Moore manifolds. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen’s plus construction with Whitehead torsions.
KW - Quillen’s plus construction
KW - homology equivalence
KW - one-sided h-cobordism
UR - http://www.scopus.com/inward/record.url?scp=84939252464&partnerID=8YFLogxK
U2 - 10.1007/s11425-014-4967-z
DO - 10.1007/s11425-014-4967-z
M3 - Article
AN - SCOPUS:84939252464
SN - 1674-7283
VL - 58
SP - 2003
EP - 2014
JO - Science China Mathematics
JF - Science China Mathematics
IS - 9
ER -