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Generalized Jiang and Gottlieb groups

  • Marek Golasiński ORCID logo EMAIL logo and Thiago de Melo ORCID logo
Published/Copyright: October 5, 2018
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Georgian Mathematical Journal
From the journal Georgian Mathematical Journal Volume 25 Issue 4

Abstract

Given a map f:X→Y, we extend Gottlieb’s result to the generalized Gottlieb group Gf⁢(Y,f⁢(x0)) and show that the canonical isomorphism π1⁢(Y,f⁢(x0))⁢→≈⁢𝒟⁢(Y) restricts to an isomorphism Gf⁢(Y,f⁢(x0))⁢→≈⁢𝒟f~0⁢(Y), where 𝒟f~0⁢(Y) is some subset of the group 𝒟⁢(Y) of deck transformations of Y for a fixed lifting f~0 of f with respect to universal coverings of X and Y, respectively.

Keywords: Deck transformation; fiber-preserving map; Gottlieb group; Jiang group; universal covering map; Whitehead center group
MSC 2010: 55Q52; 57M10; 55Q05; 55Q15

Dedicated to Tornike Kadeishvili for his 70th anniversary

Funding source: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Award Identifier / Grant number: 88881.068125/2014-01

Funding statement: Both authors are supported by CAPES–Ciência sem Fronteiras. Processo: 88881.068125/2014-01.

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Received: 2017-08-07
Accepted: 2018-05-10
Published Online: 2018-10-05
Published in Print: 2018-12-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. The extended rational homotopy theory of operads
  3. On the spectralization of affine and perfectly normal spaces
  4. Generalized Jiang and Gottlieb groups
  5. The formal Kuranishi parameterization via the universal homological perturbation theory solution of the deformation equation
  6. Cyclicity in homotopy algebras and rational homotopy theory
  7. Cyclic homology of cyclic ∞-simplicial modules
  8. An A∞-coalgebra structure on a closed compact surface
  9. The homological hexagonal lemma
  10. A twice twisted tale
  11. Algorithms in A∞-algebras
https://doi.org/10.1515/gmj-2018-0060
Keywords for this article
Deck transformation; fiber-preserving map; Gottlieb group; Jiang group; universal covering map; Whitehead center group

Articles in the same Issue

  1. Frontmatter
  2. The extended rational homotopy theory of operads
  3. On the spectralization of affine and perfectly normal spaces
  4. Generalized Jiang and Gottlieb groups
  5. The formal Kuranishi parameterization via the universal homological perturbation theory solution of the deformation equation
  6. Cyclicity in homotopy algebras and rational homotopy theory
  7. Cyclic homology of cyclic ∞-simplicial modules
  8. An A∞-coalgebra structure on a closed compact surface
  9. The homological hexagonal lemma
  10. A twice twisted tale
  11. Algorithms in A∞-algebras
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