TUESDAY, NOVEMBER 25, 2025
FRUMAM, second floor seminar room, campus Saint-Charles, Marseille
9:30
11:00
14:30
16:00
Marco GOLLA (CNRS, Université de Nantes)
Ana RECHTMAN (Université Grenoble Alpes)
Jeffrey MEIER (Washington University)
Rudy DISSLER (PhD defense, Université Aix-Marseille)
Abstracts:
Dissler: Decompositions of orientable, compact manifolds into 1–handlebodies
In this presentation, we study decompositions of smooth compact manifolds into 1—handlebodies. These decompositions are higher-dimensional generalizations of Heegaard splittings of closed 3–manifolds (introduced by Heegaard in 1898) and sutured Heegaard splittings of compact 3–manifolds with boundary (Goda, 1992). In 2016, Gay and Kirby defined trisections of closed 4–manifolds, and relative trisections of 4–manifolds with boundary, as natural extensions of such decompositions. Then, in 2023, Ben Aribi, Courte, Golla and Moussard’s notion of multisections of closed manifolds generalized trisections to higher dimensions. We show how multisections can be adapted to manifolds with boundary, introducing relative multisections, which generalize relative trisections; however, this construction induces a strong restriction on the boundary, whose connected components have to be either Sn or connected sums of copies of S1 × S(n-1). A nice feature of (relative) multisections is that they are determined by their tridimensional spine. In particular, this enables a diagrammatic representation of (relative) multisections by diagrams. Finally, we quickly introduce a possible generalization of relative multisections, pseudo-multisections, which alleviates the restriction on the boundary.