I will introduce the topic of mapping class groups of 4-manifolds, which can be studied using algebraic topology, gauge theory, and geometric methods. I will survey what is known, give an outline of some of the methods of proof, and highlight some open questions. I will particularly focus on pseudo-isotopy theory.
If a group contains a strongly contracting element, then it is acylindrically hyperbolic. Moreover, one can use the Projection Complex of Bestvina, Bromberg and Fujiwara to construct an action on a hyperbolic space where said element acts loxodromically. However, the action depends on the chosen element and other strongly contracting elements are not necessarily loxodromic. It raises the...
In this talk we will discuss a generalization of Sageev’s wallspace construction that allows to study the geometry of certain spaces by combinatorial properties of certain walls. Specifically, we’ll look at the interactions with hyperbolicity and focus on two applications. In CAT(0) spaces, these techniques allow to construct a “universal hyperbolic quotient”, called the curtain model, that is...
Virtual Artin groups were introduced a few years ago by Bellingeri, Paris, and Thiel, with the aim of generalizing the well-studied structure of virtual braid groups to the broader context of Artin groups. These fascinating objects possess a rich algebraic structure that encompasses both Coxeter groups and classical Artin groups. In this talk, we will explore the topology of virtual Artin...
I will introduce the topic of mapping class groups of 4-manifolds, which can be studied using algebraic topology, gauge theory, and geometric methods. I will survey what is known, give an outline of some of the methods of proof, and highlight some open questions. I will particularly focus on pseudo-isotopy theory.
I will introduce the topic of mapping class groups of 4-manifolds, which can be studied using algebraic topology, gauge theory, and geometric methods. I will survey what is known, give an outline of some of the methods of proof, and highlight some open questions. I will particularly focus on pseudo-isotopy theory.
Strongly invertible links are collections of disjoint oriented circles in the tri-dimensional space together with an involution preserving the components and reversing the orientation. In this talk we will introduce a family of invariants of strongly invertible links which are analogues of the sl(n) polynomials for links; in particular, they are Laurent polynomials in the variable q and are...
If a knot decomposes as a connected sum, is this decomposition visible in a diagram of the knot? We will see that the answer is "yes", for so-called alternative diagrams. This partially resolves a conjecture posed by Cromwell in 1991. The proof relies on a new criterion for the existence of fixed arcs of (partial) monodromies. No prior knowledge of monodromies or knot diagrams will be assumed....
This talk is intended as an introduction to the so called “Local-to-Global rigidity” of graphs and aims to present the links of this notion with both topology and geometry.
More precisely, a graph G is called Local-to-Global rigid if there exists R>0 such that every other graph whose balls of radius R are isometric to the balls of radius R in G is covered by G.
We’ll talk about the...
The Gordian distance u(K,K') between two knots K and K' is the minimal number of crossing changes needed to relate K and K'. The unknotting number u(K) of a knot K arises as the Gordian distance between K and the trivial knot. Rasmussen was the first to find a connection between Khovanov homology and u: his invariant s, extracted from Khovanov homology, yields a lower bound for the slice genus...
