Abstract
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.
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Su, Y., Ye, S. Fundamental groups, homology equivalences and one-sided h-cobordisms. Sci. China Math. 58, 2003–2014 (2015). https://doi.org/10.1007/s11425-014-4967-z
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DOI: https://doi.org/10.1007/s11425-014-4967-z