A primer on the group of self-homotopy equivalences: a rational homotopy theory approach

Cristina Costoya and Antonio Viruel – GJM, Volume 5, Issue 1 (2020), 76-87.

This manuscript is a revised version of the lecture notes of a course given in the 5th GeToPhyMa Summer School on « Rational Homotopy Theory and its Interactions » (July 11–21, 2016, Rabat, Morocco). It intends to be a gentle, while non trivial, introduction to the study of the group of self-homotopy equivalences from a Rational Homotopy Theory perspective. It also makes accessible some material and proofs that are not readily available in the literature.


Received: December 1, 2019.
Accepted: March 20, 2020.
Published: July 30, 2020.


Cristina Costoya
CITIC Research Center,
Departamento de Computación,
Universidade da Coruña, A Coruña, Spain
Antonio Viruel
Departamento de Álgebra, Geometría y Topología,
Universidad de Málaga,
Apdo correos 59, 29080, Málaga, Spain.


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