Geometric Topology Seminars: Bruno Martelli and José María Montesinos Amilibia (25/11/2022)
Friday 25th November 2022 - on line: https://meet.google.com/sdx-bykx-nep
at 3 p.m.: Bruno Martelli (University of Pisa), Shadows of 3- and 4-manifolds I
Abstract: A shadow is a two-dimensional cell complex designed to be thickened in 4 dimensions. This object, introduced by Turaev, communicates nicely with three facets of geometric topology that are quite distant from each other: that of smooth 4-manifolds, hyperbolic 3-manifolds, and quantum invariants. We will introduce shadows and focus mostly on the first two aspects, that is their relation with 4-manifolds and hyperbolic 3-manifolds.
at 4.30 p.m.: Josè Marìa Montesinos Amilibia (Real Academia de Ciencias Exactas, Físicas y Naturales, Spain), Integral quadratic forms: commensurability; projective equivalence and invariants
Abstract: Two integral quadratic forms are said to be commensurable if so are they groups of automorphs. And they are projectively equivalent if rational multiples of both are rationally equivalent. We will show the equivalence of these concepts when the forms are indefinite.