Fundamental groups, homology equivalences and one-sided h-cobordisms  

作　　者：SU Yang YE ShengKui 

机构地区：[1]Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences [2]Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University

出　　处：《Science China Mathematics》2015年第9期2003-2014,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grand No.10901151);RDF-13-02-08 of Xi’an Jiaotong-Liverpool University

摘　　要：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.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.

关 键 词：Quillen’s plus construction homology equivalence one-sided h-cobordism 

分 类 号：O186.12[理学—数学]