Do all 3-manifolds bound definite 4-manifolds?

par Marco Golla

mardi 11 oct. 2022, 11:00 → 12:15 Europe/Paris

Rokhlin proved that each closed oriented 3-manifold bounds a compact smooth 4-manifold, and hence plenty. Among all of these, can we always find one whose intersection form is (semi-)definite? Using Heegaard Floer correction terms and an analysis of short characteristic covectors in bimodular lattices, we give an obstruction for a 3-manifold to bound a definite 4-manifold, and produce some concrete examples. This is joint work with Kyle Larson.