Explore the intricacies of Floer homotopy theory without relying on spectra in this illuminating lecture by Mohammed Abouzaid from Columbia University. Delve into key concepts such as manifold slow category, topologically slow category, and moduli spaces. Examine the boundary conjecture and its variants, and investigate oriented groups, orbitals, K homology, and infinite spaces. Gain valuable insights into this complex mathematical topic through a comprehensive exploration of its fundamental principles and advanced applications.