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Series: Geometry Topology Seminar

Series: Geometry Topology Seminar

Series: Geometry Topology Seminar

Series: Geometry Topology Seminar

Series: Geometry Topology Seminar

Series: Geometry Topology Seminar

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Series: Geometry Topology Seminar

I will talk about homomorphisms between surface braid groups. Firstly, we will see that any surjective homomorphism from PB_n(S) to PB_m(S) factors through a forgetful map. Secondly, we will compute the
automorphism group of PB_n(S). It turns out to be the mapping class group when n>1.

Series: Geometry Topology Seminar

Certain fibered hyperbolic 3-manifolds admit a layered veering triangulation, which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. We present experimental results which shed light on the combinatorial structure of veering triangulations, and its relation to certain topological invariants of the underlying manifold. We will begin by discussing essential background material, including hyperbolic manifolds and ideal triangulations, and more particularly fibered hyperbolic manifolds and the construction of the veering triangulation.

Series: Geometry Topology Seminar

We give a simple geometric criterion for an element to normally generate the mapping class group of a surface. As an application of this criterion, we show that when a surface has genus at least 3, every periodic mapping class except for the hyperelliptic involution normally generates. We also give examples of pseudo-Anosov elements that normally generate when genus is at least 2, answering a question of D. Long.

Series: Geometry Topology Seminar

We will discuss a relation between some notions in three-dimensional topology and four-dimensional aspects of knot theory.