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

• Date: 2013
• Main Authors: de, Melo Thiago, Golasinski, M., Де, Мело Тьяго, Голасинський, М.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2488
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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_{\alpha}\left( {{{\mathbb{S}}^{n+k }},{{\mathbb{S}}^n}} \right...