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Evaluation Fibrations and Path-Components of the Mapping Space \( M\left( {{{\mathbb{S}}^{n+k }},{{\mathbb{S}}^n}} \right) \) for 8 ≤ k ≤ 13

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Ukrainian Mathematical Journal Aims and scope

Let \( M\left( {{{\mathbb{S}}^m},{{\mathbb{S}}^n}} \right) \) be the space of maps from the m-sphere \( {{\mathbb{S}}^m} \) into the n-sphere \( {{\mathbb{S}}^n} \) with m, n ≥ 1. We estimate the number of homotopy types of path-components \( M\left( {{{\mathbb{S}}^{n+k }},{{\mathbb{S}}^n}} \right) \) and the fiber homotopy types of the evaluation fibrations \( {\omega_{\alpha }}:{M_{\alpha }}\left( {{{\mathbb{S}}^{n+k }},{{\mathbb{S}}^n}} \right)\to {{\mathbb{S}}^n} \) for 8 ≤ k ≤ 13 and \( \alpha \in {\pi_{n+k }}\left( {{{\mathbb{S}}^n}} \right) \) extending the results of [Mat. Stud., 31, No. 2, 189–194 (2009)]. Further, the number of strong homotopy types of \( {\omega_{\alpha }}:{M_{\alpha }}\left( {{{\mathbb{S}}^{n+k }},{{\mathbb{S}}^n}} \right)\to {{\mathbb{S}}^n} \) for 8 ≤ k ≤ 13 is determined and some improvements of the results from [Mat. Stud., 31, No. 2, 189–194 (2009)] are obtained.

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Authors and Affiliations

  1. University of Warmia and Mazury, Olsztyn, Poland

    M. Golasiński

  2. Institute de Geociências e Ciências Exatas, São Paulo, Brazil

    T. de Melo

Authors
  1. M. Golasiński
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  2. T. de Melo
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 8, pp. 1023–1034, August, 2013.

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Golasiński, M., de Melo, T. Evaluation Fibrations and Path-Components of the Mapping Space \( M\left( {{{\mathbb{S}}^{n+k }},{{\mathbb{S}}^n}} \right) \) for 8 ≤ k ≤ 13. Ukr Math J 65, 1141–1154 (2014). https://doi.org/10.1007/s11253-014-0849-3

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  • DOI: https://doi.org/10.1007/s11253-014-0849-3

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