### Abstract

Original language | English |
---|---|

Pages (from-to) | 445-462 |

Number of pages | 18 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 59 |

Issue number | 2 |

Early online date | 26 Oct 2015 |

DOIs | |

Publication status | Published - May 2016 |

### Fingerprint

### Keywords

- homotopy groups
- self-equivalences
- equivariant spheres
- complex representations

### Cite this

**On the homotopy groups of the self-equivalences of linear spheres.** / Libman, Assaf.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 59, no. 2, pp. 445-462. https://doi.org/10.1017/S0013091515000127

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TY - JOUR

T1 - On the homotopy groups of the self-equivalences of linear spheres

AU - Libman, Assaf

PY - 2016/5

Y1 - 2016/5

N2 - Let S(V ) be a complex linear sphere of a finite group G. LetS(V )∗n denote the n-fold join of S(V ) with itself and let autG(S(V )∗)denote the space of G-equivariant self homotopy equivalences of S(V )∗n.We show that for any k ≥ 1 there exists M > 0 which depends only onV such that |k autG(S(V )∗n)| ≤ M is for all n ≫ 0.

AB - Let S(V ) be a complex linear sphere of a finite group G. LetS(V )∗n denote the n-fold join of S(V ) with itself and let autG(S(V )∗)denote the space of G-equivariant self homotopy equivalences of S(V )∗n.We show that for any k ≥ 1 there exists M > 0 which depends only onV such that |k autG(S(V )∗n)| ≤ M is for all n ≫ 0.

KW - homotopy groups

KW - self-equivalences

KW - equivariant spheres

KW - complex representations

U2 - 10.1017/S0013091515000127

DO - 10.1017/S0013091515000127

M3 - Article

VL - 59

SP - 445

EP - 462

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -