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Homotopy theory of complete Lie algebras

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Aniceto Murillo
Universidad de Málaga
Thu, 2019-05-09 09:30 - 10:30
MPIM Lecture Hall

Having as motivation the Deligne's principle by which every deformation functor is governed by a differential graded Lie algebra, we build a homotopy theory for these algebras which extend the classical Quillen approach to any topological space and is based in a new model category structure for (complete) differential graded Lie algebras. The core of this structure lies in the construction of the "Eckmann-Hilton dual" of the classical differential forms on the standard simplices. In fact, the non-existence of this object in the Lie setting has puzzled (rational) homotopy theorists since the beginning of the subject. Joint work with Urtzi Buijs, Yves Félix and Daniel Tanré.

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