The Boardman-Vogt resolution and algebras up-to-homotopy
Seminar Room 2, Newton Institute Gatehouse
AbstractIn this lecture, we will present some basic properties and constructions of topological operads and their algebras. For an operad P, the property of having a P-algebra structure is in general not invariant under homotopy: a space which is homotopy equivalent to one carrying a P-algebra structure only has a "P-algebra structure up-to-homotopy". We will address the questions whether these P-algebra structures up-to-homotopy can be controlled by another operad, and whether they can be "strictified" to true P-algebra structures. Much of this goes back to Boardman and Vogt's book "Homotopy Invariant Algebraic Structures", but can efficiently be cast in the language of Quillen model categories.
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