Binomial rings in homotopy theory
Moduli and Friends seminar
Monday 7 November 2022
Geoffroy Horel (Université Sorbonne Paris Nord) — Binomial rings in homotopy theory
In a famous paper, Sullivan showed that the rational homotopy theory of finite type nilpotent spaces can be encoded in a fully faithful manner by mapping it to the homotopy category of commutative differential graded algebras over the rational numbers. For integral homotopy theory, a result of Mandell shows that it is faithfully captured by the integral cochains equipped with their E-infinity structure. This functor is however not full. I will explain a way of fixing this problem inspired by work of Toën, using cosimplicial binomial rings instead of E-infinity differential graded algebras.
* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.