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Mixed Hodge structures and formality of symmetric monoidal functors by Cirici, Joana; Horel, Geoffroy is a scholarly article available to read on EtoBox.

What is Mixed Hodge structures and formality of symmetric monoidal functors about?

We use mixed Hodge theory to show that the functor of singular chains with rational coefficients is formal as a lax symmetric monoidal functor, when restricted to complex schemes whose weight filtration in cohomology satisfies a certain purity property. This has direct applications to the formality of operads or, more generally, of algebraic structures encoded by a colored operad. We also prove a dual statement, with applications to formality in the context of rational homotopy theory. In the general case of complex schemes with non-pure weight filtration, we relate the singular chains functor to a functor defined via the first term of the weight spectral sequence.

Author

Cirici, Joana; Horel, Geoffroy

Published

2017

Language

EN