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A theorem of Kontsevich on graph complexes and some applications in topology
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There are several interesting results in somewhat different aspects of algebraic topology that involve chain complexes that are defined via graphs and certain graph operations. For example, Watanabe produced non-trivial elements in the rational homotopy groups of Diff(Dₙ) beyond the known stable range, and Berglund and Madsen showed that they appear in the stable cohomology of certain moduli spaces. A good interpretation of the emergence of these graph complexes is via (cyclic) operads. I want to discuss this definition and some of the results by Kontsevich on their homology that relate them to some problems in topology.
This talk is part of the Junior Geometry Seminar series.
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