Floer homotopy theory SMS, July 2022: notes and exercises

This page collects some notes and exercises from the Séminaire de Mathématiques Supérieures on Floer homotopy theory, held at PIMS, UBC, Vancouver in  July 2022. The official webpage is here (starting sometime later in summer 2022, it should include links to videos of those talks which were recorded). Various links point to this website, so I will keep the notes up for the foreseable future.

If you have any feedback on these, please contact the lecturer(s) directly. Please also credit them as appropriate when re-using these.

Fundamentals of Floer Homology, Nathaniel Bottman and Catherine Cannizzo

• Catherine's lectures: L1, L3, L5, L9

• Catherine's exercises: E1, E3, E5, E9 and solutions 

• Nate's handwritten notes: L2, L4, L6, L7, L8

• Nate's typed exercises & notes: L2+E2, L4+E4, E6, E7 (there are no exercises for L8)

Operads and Ring Spectra, Hiro Lee Tanaka

• Notes and exercises

String topology, Kate Poirier

• Lecture notes

• Exercises

Spectra and smash products, Cary Malkiewich

• Lecture outline and problem sets

• Slides (NB: these were used to punctually complement the chalk talks)

• Handwritten notes (A. Keating): L1, L2, L3, L4

Applications of Floer homology, Jeff Hicks

• L1 + E1 (incl. solutions), Exact sequences in symplectic geometry

• L2 + E2, Heegaard Floer theory

• L3 + E3, Symplectic cohomology

Floer homotopy theory, Mohammed Abouzaid

• Problem sets: E1, E2+E3

• Notes by Amanda Hirschi