Alex Takeda: Modeling constant loops and simplicial string topology

Abstract.

 In joint work with M. Rivera and Z. Wang, we have described a new approach to defining string topology operations, using a certain type of algebraic duality structure called a pre-Calabi-Yau structure. I will discuss how to this formalism, applied to a dg category modeling paths in a triangulated space, gives a simplicial approach to string topology. For that, it is important to be able to model the map X -> LX given by the inclusion of constant loops; we find a very nice form for this map by using a 2-dimensional generalization of Turaev’s definition of “spider” or “Euler structure”, in the case of spaces with vanishing second homotopy group.