The Geometric Ideas of René Thom Related to Manifolds with Singularities

Explore the geometric ideas of René Thom related to manifolds with singularities in this 51-minute lecture by Dennis Sullivan from the Institut des Hautes Etudes Scientifiques (IHES). Delve into two significant papers by Thom, beginning with his renowned work from the 1950s published in "Commentarii Mathematici Helvetici." Discover the lesser-known originating problem behind this paper while examining its celebrated methods of transversality and cobordism. Then, investigate Thom's 1960s paper in "BAMS," which fully elucidates the concept of "manifolds with singularities" through manifold strata with locally constant transversal structure. Gain insights into examples and ideas that reveal how this context is rougher than smooth yet at least as effective as topological approaches. Join Sullivan, from the City University of New York's Graduate Center, as he unravels these complex mathematical concepts and their implications in the field of geometry.