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 fun...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.展开更多
基金supported by National Natural Science Foundation of China(Grand No.10901151)RDF-13-02-08 of Xi’an Jiaotong-Liverpool University
文摘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.
