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Loop spaces and E_k algebras

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If you have a question about this talk, please contact Adrian Dawid .

Loop spaces (:= based homotopy classes of maps from the circle) are fundamental objects in algebraic topology. They admit a binary operation that is “associative and to-some-level-commutative, up to coherent higher homotopy”. The thing inside parenthesis can be made formally into the statement that a k-fold loop space is a E_k algebra in spaces ( ~= spaces with an action of configuration of cubes in R^k). Under some conditions the converse is also true.

This talk will introduce basic definitions in the theory, give a lot of examples, and make the paragraph above precise. If time permits, we shall also see some E_k algebras not arising as loop spaces (e.g. some algebraic examples), and maybe homological features of those.

This talk is part of the Junior Geometry Seminar series.

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