17 citations · 42 across the 23 of their papers we have counts for
4 papers · 1 filter
An algebraic model for the free loop space
Manuel Rivera
We describe an algebraic chain level construction that models the passage from an arbitrary topological space to its free loop space. The input of the construction is a categorical…
The simplicial coalgebra of chains under three different notions of weak equivalence
George Raptis, Manuel Rivera
We study the simplicial coalgebra of chains on a simplicial set with respect to three notions of weak equivalence. To this end, we construct three model structures on the category…
String topology in three flavours
Florian Naef, Manuel Rivera, Nathalie Wahl
We describe two major string topology operations, the Chas-Sullivan product and the Goresky-Hingston coproduct, from geometric and algebraic perspectives. The geometric constructio…
Categorical models for path spaces
Emilio Minichiello, Manuel Rivera, Mahmoud Zeinalian
We establish an explicit comparison between two constructions in homotopy theory: the left adjoint of the homotopy coherent nerve functor, also known as the rigidification functor,…