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.

### Fall 2018

**Date:** September 7 2018

**Speaker:** Jens Harlander

**Title:** Some conjectures in 2-dimensional combinatorial topology

**Abstract:** In the early part of the 20th century a variety of homotopy notions emerged, such as simple homotopy, combinatorial in nature, or the homotopy theory of chain complexes, algebraic and part of homological algebra. It is well understood how the different notions relate to each other, and what obstructions exist for direct comparisons. However, fundamental open problems remain, particularly in dimension 2, where questions concerning group presentations enter the discussion. I will talk about three conjectures in dimension 2.

**Date:** September 28 2018

**Speaker:** Jens Harlander

**Title:** What is homological group theory?

**Date:** October 26 2018

**Speaker:** Kennedy Courtney

**Title:** Topological Invariants of Food Webs

**Abstract:** A food web is an interconnected network of food chains in an ecosystem. Food webs are easily modeled by directed graphs and have been well-studied from the graph theoretic perspective. However, viewing food webs as graphs does not seem to easily reveal qualities that are important in ecology. We seek to address this problem by analyzing graphs of food webs through a more sophisticated topological approach, namely through the directed forest complex.

**Date:** November 30 2018

**Speaker:** Uwe Kaiser

**Title:** Topological complexity and motion planning

**Abstract:** I will give several definitions of the topological complexity of a configuration space due to Michael Farber. These are related to motion planning in that space. I will discuss how they compare with each other, homotopy invariance, upper and lower bounds, and show several examples.

### Spring 2019

**Date:** January 25 2019

**Speaker:** Jens Harlander

**Title:** The Corson/Trace characterization of diagrammatic reducibility

**Abstract:** It is difficult to tell from a given presentation P if the group presented G(P) is finite or infinite. If the associated 2-complex K(P) exhibits a strong asphericity condition, diagrammatic reducibility, then G(P) is trivial or infinite. How do we decide G(P)=1 in the presence of DR? In 2000 Corson and Trace gave a surprisingly simple and checkable answer which I will share in my talk.

**Date:** February 1 2019

**Speaker:** Jens Harlander

**Title:** The Corson/Trace characterization of diagrammatic reducibility, 2

**Date:** March 8 2019

**Speaker:** Stephan Rosebrock, PH Karlsruhe, Germany

**Title:** On the asphericity of labeled oriented trees

**Abstract:** The Whitehead conjecture asks whether a subcomplex of an aspherical 2-complex is alwaysaspherical. This question is open since 1941. Howie has shown that the existence of a finite counterexample implies (up to the Andrews-Curtis conjecture) the existence of a counterexample within the class of labelled oriented trees. Labelled oriented trees are algebraic generalisations of Wirtinger presentations of knot groups. In this talk we start with an introduction into the field. Then we present several possibilities to show asphericity in the class of labelled oriented trees. There are many known classes of aspherical LOTs given by the weight test of Gersten, the I-test of Barmak/Minian, LOTs of Diameter 3 (Howie), LOTs of complexity two (Rosebrock) and several more.We introduce a new notion of relative asphericity and proove with this notion the asphericity of injective labelled oriented trees.

**Date:** April 5, 2019

**Speaker:** Uwe Kaiser

**Title:** Obstructions to ribbon concordance

**Abstract:** I will discuss the concept of ribbon concordance and how it relates to concordance and to the infamous slice-ribbon conjecture. Then I will state some classical results by Cameron Gordon, and survey a recent paper by Ian Zemke, which contains several interesting corollaries concerning crossing numbers.