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

Yang Su; Sheng Kui Ye

doi:10.1007/s11425-014-4967-z

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

Yang Su^*
, Sheng Kui Ye

^*Corresponding author for this work

Chinese Academy of Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2003-2014
Number of pages	12
Journal	Science China Mathematics
Volume	58
Issue number	9
DOIs	https://doi.org/10.1007/s11425-014-4967-z
Publication status	Published - 17 Sept 2015

Keywords

Quillen’s plus construction
homology equivalence
one-sided h-cobordism

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10.1007/s11425-014-4967-z

Cite this

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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{\textquoteright}s plus construction with Whitehead torsions.",

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AU - Ye, Sheng Kui

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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 - https://www.scopus.com/pages/publications/84939252464

U2 - 10.1007/s11425-014-4967-z

DO - 10.1007/s11425-014-4967-z

M3 - Article

AN - SCOPUS:84939252464

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VL - 58

SP - 2003

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JO - Science China Mathematics

JF - Science China Mathematics

IS - 9

ER -

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

Abstract

Keywords

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