Matemale Spring School 2024
New constructions of exotic 4-manifolds
May 27-31
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This year, we will study a recent paper by Levine, Lidman and Piccirillo: "New constructions and invariants of closed exotic 4-manifolds". 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 Marco Golla for his help in elaborating the program.
The event is supported by the Réseau thématique RTop (RT2171), the Mathematics Institute of Toulouse, the CIMI and the ANR JCJC SyTriQ.
The paper of Levine, Lidman and Piccirillo gives new methods to construct and distinguish pairs of exotic 4-dimensional manifolds (an exotic pair is the datum of two smooth manifolds that are homeomorphic but not diffeomorphic). Their constructions are more elementary and explicit than the previously known constructions, and produce exotic pairs with new properties. New invariants are constructed, using Heegaard-Floer homology, that allow to distinguish these exotic pairs. We will start from the prerequisites, in particular Kirby calculus and Heegaard-Floer homology.
More details and references here: program.
Organizers :
Thomas Fiedler (Institut de Mathématiques de Toulouse)
Phone number: +33 695784972
Delphine Moussard (Institut de Mathématiques de Marseille)
If you are willing to participate, please contact us by email.
List of talks:
Handle decompositions and Heegaard splittings (Julie Reina)
Kirby diagrams (Oguz Savk)
Kirby calculus and 3-dimensional surgery presentations (Butian Zhang)
Intersection form and exotic pairs (Vincent Florens)
Building blocks for the construction of exotic pairs (Jennifer Brown)
Cobordism construction of exotic manifolds (Edwin Kitaeff)
Equivariant intersection form and homeomorphisms (Anthony Saint-Criq)
Definition of HF, degree, involution ι, examples I (Chun-Sheng Hsueh)
Definition of HF, degree, involution ι, examples II (Romain Saunier)
Cobordism application and definition of α (Benjamin Haïoun)
Exact triangle (Lisa Lokteva)
Adjunction inequality (Livio Ferretti)
An explicit computation (Marco Golla)
Lemmas on HF I (Valentina Bais)
Lemmas on HF II (Gregor Masbaum)
Fireworks (Raphaël Zentner)
Talks start on Monday morning and end on Friday at noon. Accommodation is planned from Sunday evening to Friday lunch.
Registration is now closed.
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.
We will cover the stay of all participants. You are supposed to have your own funding for travel expenses, but do not hesitate to contact us if you have difficulties.
List of participants:
Valentina Bais
Thiago Brevidelli Garcia
Jennifer Brown
Anthony Christiana
Ben Clingenpeel
Livio Ferretti
Thomas Fiedler
Vincent Florens
Marco Golla
Benjamin Haïoun
Chun-Sheng Hsueh
Edwin Kitaeff
Lisa Lokteva
Gregor Masbaum
Alleysson Mathis
Joris Moulai
Delphine Moussard
Stepan Orevkov
Julie Reina
Anthony Saint-Criq
Romain Saunier
Oguz Savk
Shahnaz Shamim
Gaëtan Simian
Adrian Ticona Delgado
Vladimir Vershinin
Sardor Yakupov
Raphaël Zentner
Butian Zhang
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