Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SELF-HOMOTOPY EQUIVALENCES OF MOORE SPACES DEPENDING ON COHOMOTOPY GROUPS

  • Choi, Ho Won (Institute of Natural Science Korea University) ;
  • Lee, Kee Young (Division of Applied Mathematical Sciences Korea University) ;
  • Oh, Hyung Seok (Department of Mathematics Korea University)
  • Received : 2018.10.12
  • Accepted : 2019.01.24
  • Published : 2019.09.01
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Abstract

Given a topological space X and a non-negative integer k, ${\varepsilon}^{\sharp}_k(X)$ is the set of all self-homotopy equivalences of X that do not change maps from X to an t-sphere $S^t$ homotopically by the composition for all $t{\geq}k$. This set is a subgroup of the self-homotopy equivalence group ${\varepsilon}(X)$. We find certain homotopic tools for computations of ${\varepsilon}^{\sharp}_k(X)$. Using these results, we determine ${\varepsilon}^{\sharp}_k(M(G,n))$ for $k{\geq}n$, where M(G, n) is a Moore space type of (G, n) for a finitely generated abelian group G.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea(NRF)

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