Alexander Berglund: Rational Homotopy Theory of Mapping Spaces
The space of loops LX in a space X is an example of a mapping space: LX = map(S^1,X). This course will provide tools for computing the rational homology and homotopy groups of LX and, more generally, mapping spaces map(K,X) where K is an arbitrary finite CW-complex. In particular, we will discuss the approach using L-infinity algebras presented in arxiv.org/1110.6145
A note on prerequisites:
Some basic knowledge of rational homotopy theory would be advantageous (simplicial de Rham algebra, Sullivan models), though I will give a brief review of the necessary concepts. No prior knowledge of L-infinity algebras will be assumed.
For background on rational homotopy theory, here are some references:
Lecture notes from a course
A standard textbook:
Y. Félix, S. Halperin, J-C. Thomas
Rational homotopy theory
Graduate texts in mathematics 205, Springer
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