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      cerf theory learning seminar (fall 2025)
organized by myself and Audrick Pyronneau
fridays at 2 in pma 12.166
mailing list: cerftheory@utlists.utexas.edu



      schedule
week 1 (9/12): review of Morse theory with a view towards Cerf theory (Audrick)
week 2 (9/19): Cerf chapter I, the stratification of function space and codimension (Abhishek, notes)
week 3 (9/26): Hatcher-Wagoner chapter I, pseudoisotopies and Cerf graphics (Peter)
week 4 (10/3): Hatcher-Wagoner chapter I, independence of trajectories (Daniel)
week 5 (10/10): Cerf chapter II, crossing paths (John)
week 6 (10/17): office hours
week 7 (10/24): Hatcher-Wagoner chapter V, deformations of the graphic (Adrian)
week 8 (10/31): the pseudoisotopy theorem (Ansel)
week 9 (11/7): pseudoisotopy theory applied to 4-manifolds (Audrick)
week 10 (11/14): the sum square move (Nathan)



      sources
pseudo-isotopies of compact manifolds (Hatcher-Wagoner), the foundational (english) text on pseudoisotopy theory. includes the missing page 138 from the numdam scan
la stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie (Cerf), english summary, the foundational (french) text on pseudoisotopy theory
sur les difféomorphismes de la sphère de dimension trois (Γ₄=0) (Cerf), the paper that proved the mapping class group of S³ is trivial
a calculus for framed links in S³ (Kirby), the paper that invented Kirby calculus
topological models in biology (Thom), apparently a foundational paper in singularity theory
pseudo-isotopy and diffeomorphisms of the 4-sphere I: loops of spheres (Gabai-Gay-Hartman)



      fun fact
you don't pronounce the f in Cerf, so it's pronounced the same as Serre (from Raphaël Cerf via Danny Ruberman)



      official seminar song
surf's up by the beach boys