Hochschild cohomology of Sullivan algebras and mapping spaces

Gatsinzi, J.-B.

doi:10.1016/j.ajmsc.2018.07.002

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Hochschild cohomology of Sullivan algebras and mapping spaces

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Gatsinzi, J.-B.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.ajmsc.2018.07.002
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Gatsinzi, J.-B. (2019). Hochschild cohomology of Sullivan algebras and mapping spaces. Arab Journal of Mathematical Sciences, 25(1), 123-129. doi:10.1016/j.ajmsc.2018.07.002.

Cite as: https://hdl.handle.net/21.11116/0000-0004-A110-3

Abstract

Letf:X→Ybe a map between simply connected spaces having the homotopyof finite type CW-complexes, whereH∗(Y,Q) is finite dimensional andφ:(∧V,d)→(B,d) a Sullivan model off. We consider (B,d) as a module over∧Vvia the mappingφ.Let map(X,Y;f) denote the component offin the space of mappings fromXtoY. In thispaper we show that there is a canonical injectionπ∗(Ωmap(X,Y;f))⊗Q→H H∗(∧V;B).