Matemale Spring School 2026
Knotted 3-balls in the 4-sphere
June 08-12
Matemale Spring School 2026
Knotted 3-balls in the 4-sphere
June 08-12
The school is designed for Master students, PhD students and researchers, younger and older. Participants are encouraged to choose a (not yet attributed) talk in the list. We are grateful to Ryan Budney for his help in elaborating the program.
The event is supported by the Réseau thématique RTop (RT2171), the Mathematics Institute of Toulouse, the LMAP (University of Pau), the IMAG (University of Montpellier), Occimath (fédération occitane de mathématiques) and the LabEx PERSYVAL (Université Grenoble Alpes).
If you wish to participate, please pre-register there by March 31. Acceptance and financial support will be confirmed shortly after the deadline.
The aim of this workshop is to describe the non-finite-generation of various homotopy groups of automorphism groups of manifolds, specifically products of a circle and a ball. The techniques use classical intersection theory. We discuss how one can compute in the homotopy groups of spheres, and later wedges of spheres, using transversality. We will study the construction of the so-called W3-invariant of automorphisms of manifolds. We will see how one computes it using knowledge of the homotopy-groups of configuration spaces, which are related to wedges of spheres. We will finish the workshop discussing some applications of these techniques.
More details and references here: program.
List of talks:
Homotopy groups of spheres, framed cobordism, part I
Homotopy groups of spheres, framed cobordism, part II
Hilton-Milnor and the homotopy groups of wedges of spheres
Embedding spaces, tubular neighbourhoods, diffeomorphism groups and fibrations
Spaces of unknots and Cerf's observations on the diffeomorphism group of S^1 x D^{n-1}
Smale and Cerf's proof of Smale's theorem on diffeomorphisms of the 2-sphere
Spaces of embeddings and the discovery of barbell diffeomorphisms
Implanting barbell diffeomorphisms, and detection
A warm-up talk on W3
Computing the W3-invariant I
Computing the W3-invariant II
What can be said about Diff(S^1 x D^{n-1}) for n>5? Pseudo-isotopy and comparison with Hatcher-Wagoner. (Ryan Budney)
Gabai-Gay-Hartman's work on pseudoisotopy diffeomorphisms of the 4-sphere (David Gabai)
Tatsuoka's results on splitting spheres
A type-2 invariant of 2-knots
Organizers :
Ryan Budney (University of Victoria)
Thomas Fiedler (Université de Toulouse)
Vincent Florens (Université de Pau et des pays de l'Adour)
David Gabai (Princeton University)
Delphine Moussard (Université Grenoble Alpes)
Hoël Queffelec (CNRS)
Talks start on Monday morning and end on Friday at noon. Accommodation is planned from Sunday evening to Friday lunch.
We will be accommodated in the Centre de vacances "La Capcinoise" (https://www.lacapcinoise.fr/). This is just for information, you don't need to make a reservation by yourself. Beware that towels and soap are not provided, and rooms are shared.
To reach Matemale, you can come by train to Mont-Louis La Cabanasse, and there we'll pick you up by car. Another possibility is to find another participant going to Matemale by car from Toulouse, Montpellier or Perpignan, and who has a place for you. For more information on this possibility, please contact the organizers by email.
We will cover the stay of the participants, in the limit of available funding.
List of participants: TBC