# Topology Seminar

The Topology Seminar will meet on Fridays, usually alternating with the AGC seminar, 3:00 p.m. – 4:00 p.m. in room MB 124 (Mathematics Building). Below you find the information for the topology talks. Everybody who is interested is invited to join. Please contact Jens Harlander (jensharlander@boisestate.edu) for more information.

You can also view selected Topology Seminar Archives.

**Date:** September 6, 2019

**Speaker: **Allison Arnold-Roksandich, BSU

**Title: **Normal Mathematics

**Abstract:** What is normal? It changes based upon what context we’re in. The goal of this talk is to discuss these varying definitions and see the thread that runs between them. This is not a complete thread at this time, but should be a nice start point for the discussion.

**Speaker:** Kennedy Courtney, BSU

**Title: **Index and the Poincare-Hopf Theorem

**Abstract: **We will take a look at vector fields and color mappings as geometric realizations of a complex function. We will explore methods of finding the index of a closed curve in the domain of a meromorphic function. This will lead to the Poincare-Hopf Theorem:

Let $V$ be a vector field on a manifold without boundary such that $V$ has only isolated zeros. Then the number of zeros of the vector field is equal to the Euler characteristic of the manifold.

**Date:** October 18, 2019

**Speaker:** Uwe Kaiser, BSU

**Title:** Roots of the Alexander polynomial and orderability of 3-manifold groups

**Abstract:** In 2013 Boyer, Gordon and Watson formulated an important conjecture in low-dimensional topology, now known as the L-space conjecture, relating orderability of 3-manifold groups with geometric properties and Heegaard-Floer homology of the 3-manifold. In the case of Dehn surgery on knot complements in homology 3-spheres the conjecture leads in many cases to questions about the existence of simple roots of the Alexander polynomial of the knot. I will try to give the definitions necessary to state the L-space conjecture and to explain (without any details) the relation to the Alexander polynomial.

**Date:** November 1, 2019

**Speaker:** Jens Harlander, BSU

**Title:** Locally indicable groups

**Abstract:** A group is called indicable if it maps onto the infinite cyclic group Z. Geometric group theorists like indicable groups, because the mapping onto Z provides the group with a direction, also thought of as a height function. A full ordering would be even better, but to get there the notion of indicability needs to be strengthened. A group is called locally indicable if every non-trivial finitely generated subgroup is indicable. It turns out that locally indicable groups are orderable (a topic for another day). In my talk I will show that knot groups are locally indicable.

**Date:** November 15, 2019

**Speaker:** Kennedy Courtney, BSU

**Title:** The Directed Forest Complex and Shellability

**Abstract:** The directed forest complex is a simplicial complex built from directed forests of a digraph. We explore the homotopy type of certain rooted subcomplexes of the directed forest complex as well as the homotopy type of the directed forest complex in the case that the base digraph is acyclic.

**Date:** December 6, 2019

**Speaker: **Uwe Kaiser, BSU

**Title: ** Quantum modularity and quantum knot invariants

**Abstract:** I will state Zagier’s quantum modularity conjecture for the colored Jones polynomial of a knot and discuss the relation with Kashaev’s volume conjecture. I will discuss why these conjectures are important and try to give at least an idea of most of the necessary definitions. Presently the conjecture has been proved only for the figure 8 knot, even though many explicit computations for the colored Jones polynomial and also many results about the hyperbolic volumes of knots are known.