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Explore a one-hour lecture on extending the Pontryagin-Thom construction to the entire stable homotopy category. Delve into joint work with Andrew Blumberg that aims to build foundations for Floer homotopy. Examine how this research expands the relationship between stable homotopy groups and framed bordism groups to encompass objects, morphisms, and compositions within the stable homotopy category. Begin by investigating the challenge of developing a Morse theoretic description of bordism groups, and discover how this approach provides new insights into the structure of stable homotopy theory.
