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Alex Takeda: Modeling constant loops and simplicial string topology

Time: Thu 2024-02-15 13.15 - 14.15

Location: Cramer room, Albano

Participating: Alex Takeda (Uppsala University)


 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.