Braids and diffeomorphisms (ICMU School 27 July - 5 August 2026)
In the summer of 2026, I gave a series of lectures on Braids and Diffeomorphisms for PhD students at the ICMU Summer School on Links, Braids and Diffeomorphisms of Surfaces. The guiding theme was the construction of quasi-morphisms on diffeomorphism groups of manifolds due to Gambaudo and Ghys, generalised and developed by Brandenbursky. I used it as a motivation to learn the basics on braid groups, quasi-morphisms and diffeomorphism groups of manifolds.References
- My lecture notes
- Misha Brandenbursky
- D.Burago, S.Ivanov, L.Polterovich "Conjugation-invariant norms of geometric origin"
- D.Calegari "scl"
- Compact-open topology
- Fibration
- Fibre bundle
- Ś.R. Gal "Euler characteristic of the configuration space of a complex"
- J.-M.Gambaudo and E.Ghys "Commutators and diffeomorphisms of surfaces"
- Homotopy groups
- K.Mann "A short proof that Diffc(M) is perfect"
- K.Mann "Minicourse: The algebraic structure of diffeomorphism groups"
- L.Polterovich "Floer homology, dynamics and groups"
- Presentation of a group
Birds I saw in the Sataniv region during my visit:
Barn swallow, Blackbird, Black kite, Black redstart, Black woodpecker, Blue tit, Booted eagle, Chaffinch, Chiffchaff, Collared Dove, Common buzzard, Common redstart, Eurasian Treecreeper, Goldfinch, Goshawk, Great spotted woodpecker, Great tit, Greenfinch, Green woodpecker, Grey-headed woodpecker, Grey heron, Hawfinch, House martin, House sparrow, Kestrel, Kingfisher, Long-tailed tit, Mallard, Marsh tit, Middle spotted woodpecker, Raven, Red breasted flycatcher, Robin, Song thrush, Sparrowhawk, Spotted flycatcher, Stonechat, Swift, Tree sparrow, Willow tit, Willow warbler, WoodpigeonMy home page