Koszul duality in algebraic topology - an historical perspective

Details Koszul duality in algebraic topology - an historical perspective Koszul duality in algebraic topology - an historical perspective

2010-01-12

arxiv.org/abs/1001.2032v1

Mathematics

Algebraic Topology

From a presentation given at the Luminy conference on operads in 2009. 9 pages, two figures

Scientific paper

We survey the topology which led to the original bar and cobar constructions, for both associative algebras and coalgebras and for Lie algebras and commutative coalgebras. These constructions are often viewed as part of the larger theory of Koszul duality of operads, so this survey is meant to offer an historical perspective on the most prominent cases of that theory. We also explain recent work which shows that Hopf/linking invariants for homotopy are at the heart of the duality between commutative algebras and Lie coalgebras.

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