7. Dezember 2021
Thomas Rot (Vrije Universiteit Amsterdam)
Proper homotopy classes of non-linear Fredholm mappings
Many PDE problems can be formulated as finding zero sets of non-linear (proper) Fredholm mappings f:M -> H where M is a Hilbert manifold, and H is a Hilbert space. In this talk I will discuss a complete invariant for these mappings. This invariant is based on an idea from classical finite dimensional differential topology: framed cobordism and the Pontryagin-Thom construction. In this talk I will recall this construction and discuss how the Pontryagin-Thom construction has to be modified to be useful in the infinite dimensional world. No previous knowledge about differential topolgy (framed cobordism and the Pontryagin-Thom construction) will be assumed. This is joint work with Alberto Abbondandolo.