Doktorandseminarium: Associativity in topology

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Johan Asplund
  • Kontaktperson: Volodymyr Mazorchuk
  • Seminarium

Abstract:

Many algebraic constructions stemming from topology such as various (co)homology theories and homotopy groups naturally carry operations that are associative, and often one might take associativity for granted. However, if one relaxes the associativity requirement and allows associativity to only hold up to "higher homotopy" we get structures that are called A∞-structures.

The goal for this talk is to introduce the definition of an A∞-algebra and see how it naturally arises from the study of homotopy theory of loop spaces. My key motivation for studying A∞-structures comes from the Fukaya category in symplectic topology, which is an A∞-category and plays an important role in homological mirror symmetry.