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WRAZIDLO, Dominik Johannes/ JSPS Postdoctoral Fellowships for Research in Japan



WRAZIDLO, Dominik Johannes WRAZIDLO, Dominik Johannes(JSPS Postdoctoral Fellowships for Research in Japan) My areas of research are differential and algebraic topology, particularly global singularity theory of differentiable maps, and also topology of stratified spaces. More specifically, my recent work relates the study of so-called fold maps to the theory of high-dimensional manifolds, especially to exotic spheres. Exploiting the topological impact of fold index constraints, I have introduced two new natural subgroup filtrations of the group of homotopy spheres. By employing an innovative palette of techniques ranging from parametrized Morse theory
to symplectic geometry, I have shown that these filtrations capture plenty of essential phenomena of geometric topology. Among these are Milnor and Kervaire homotopy spheres studied in surgery theory, Banagl's framework of positive TFTs, as well as the Gromoll filtration that connects to differential geometry.

Keyword Special Generic Map, Homotopy Sphere, Gromoll Filtration, Positive TFT, Intersection Homology
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