Geometric Topology Seminars 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.: Josč Marģa Montesinos Amilibia (Real Academia de Ciencias Exactas, Fķsicas 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.
Friday 2nd December 2022
at 4.30 p.m.: Josč Marģa Montesinos Amilibia (Real Academia de Ciencias Exactas, Fķsicas y Naturales, Spain), Integral quadratic forms: invariants for projective equivalence
Abstract: Two integral quadratic forms are projectively equivalent if and only if a finite set of invariants, readily computable, coincide. The odd and even dimensional cases are strikingly different. The invariants are related to the so called Conway excesses invariants of rational equivalence.
Wednesday 14th December 2022
at 3 p.m.: Daniele Zuddas (University of Trieste), Compact topological 4-manifolds are finitely presentable
Abstract: Compact PL manifolds can be determined by a finite data set, that is a triangulation. On the other hand, compact topological 4-manifolds that are known to be not PL arise as the result of infinite constructions such as Casson handles. So it is natural to ask whether compact topological 4-manifolds can be determined by a finite data set. In this talk we answer in the affirmative. I will try to make the talk as much accessible as possible. This is a joint work with Micheal Freedman.
at 4.30 p.m.: Bruno Martelli (University of Pisa), Shadows of 3- and 4-manifolds II
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.