SMALL TRIANGULATIONS OF 4-MANIFOLDS, THE 4-MANIFOLD CENSUS, AND 2-KNOTS
SMALL TRIANGULATIONS OF 4-MANIFOLDS, THE 4-MANIFOLD CENSUS, AND 2-KNOTS
Data evento: 12 Novembre 2025 - 16.00
Dove: aula M1.3
Speaker: Dott. R.A. Burke (University of Oxford)
Abstract: We present a framework to classify PL-types of large censuses of triangulated 4-manifolds, which we use to classify the PL-types of all triangulated orientable 4-manifolds with up to 6 pentachora. This is successful except for triangulations homeomorphic to the 4-sphere, complex projective plane, and a particular rational homology sphere, where we find at most four, three, and two PL-types respectively. We conjecture that they are all standard. In the first half of this talk, I will discuss some of the ideas behind these results. In the second half I will focus on the combinatorial structure of the triangulations still resisting classification, and how these relate to ongoing work concerned with 2-knots — which we consider interesting in its own right.