Aula Seminari - Dipartimento di Matematica
A shadow of a closed 4-manifold is a 2-complex suitably embedded in the 4-manifold, which can be treated as a combinatorial description of 4-manifolds. An invariant, called the shadow-complexity, of 4-manifolds is defined by counting certain vertices in shadows. On the other hand, a trisection is a decomposition of a 4-manifold into three handlebodies, and the intersection of the three handlebodies forms an orientable surface called the trisection surface. The trisection genus of a 4-manifold is defined as the minimum genus of all trisection surfaces. In this talk, we introduce a refined version of the shadow-complexity and give an inequality between the complexity and the trisection genus. Furthermore, we determine the complexity we introduced for some 4-manifolds. This is joint work with Masaki Ogawa.