## Geometry Seminar - Abstracts

### Talk

Wednesday 24 January 2018, 16:00-17:00 in HG03.085

**Gijs Heuts** (Universiteit Utrecht)

*Lie algebras and periodicity in homotopy theory*

### Abstract

Quillen introduced the use of Lie algebras to study
homotopy theory. He associated to every space X a differential
graded Lie algebra over the rational numbers from which all rational
invariants of X (e.g. rational cohomology and homotopy groups) can
be calculated, thus translating the study of rational homotopy
theory into algebra. The torsion in the homotopy groups of a space
is generally harder to understand. It can be organized into certain
periodic families and I will discuss how Lie algebras can be used to
describe these as well.

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