Geometry and topology: Non-linear Fredholm mappings and homotopy theory

  • Date:
  • Lecturer: Thomas Rot (UV Amsterdam)
  • Contact person: Georgios Dimitroglou Rizell and Maksim Maydanskiy
  • Seminarium

Abstract: Non-linear existence problems can attacked with topological methods. For example a map between closed manifolds of the same dimension is surjective if the degree is non-zero. The degree is a homotopy invariant and two mappings into the sphere are homotopic if and only if the degrees are equal. Framed cobordism is a generalization for maps between closed manifolds of different dimensions. Again homotopy classes into the sphere are fully captured by the Framed cobordism class. In this talk I will discuss joint work with Alberto Abbondandolo in which we generalize the theory to an infinite dimensional setting.