Tamás Terpai

Rényi Institute

Representing homology by nice maps

Constructions of maps between manifolds often end up producing highly singular maps, with lots of geometric data obscured by their non-generic nature. We explore the general theme of changing maps to less singular ones, mainly by cobordism, using classifying spaces of singular maps, and present recent results (both positive and negative) concerning representing cohomology classes by maps with a prescribed set of singularities.