### The Boardman-Vogt resolution and algebras up-to-homotopy

Moerdijk, I *(Radboud Universiteit Nijmegen)*

Wednesday 09 January 2013, 15:30-16:30

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

In 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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