Tuesday, January 11, 14:00
Manuel Rivera (Purdue University), An algebraic model for the free loop space.
I will describe a functorial algebraic construction that models
the passage from a topological space to its free loop space, without
imposing any restrictions on the fundamental group of the underlying space.
The input of the construction is a curved coalgebra with certain extra
structure reminiscent of the linear dual of a B-infinity algebra. The
construction to be discussed is a modified version of the coHochschild
complex which takes this coalgebraic structure as input. This builds upon a
framework for categorical Koszul duality recently proposed by Holstein and
Lazarev. When the construction is applied to the coalgebra of chains,
suitably interpreted, of an arbitrary simplicial set X one obtains a chain
complex that is quasi-isomorphic to the chains on the free loop space of the
geometric realization of X. This extends classical results regarding models
for the free loop space of a simply connected space in terms of Hochschild