[Aalto AGC Seminar] Gerald Williams (University of Essex) | Cyclic presentations of groups, knot groups, LOG groups, and 3-dimensional manifolds | Mon 23.6. at 14:15

[Aalto Algebra, Geometry and Combinatorics Seminar]

We would like to invite you to a talk in the Aalto AGC (Algebra, Geometry and Combinatorics) Seminar.

The talk is on
Tue 23.6. at 14:15-15:00
in
M3 (M234), Otakaari 1.

The speaker is
Gerald Williams (University of Essex)
giving the talk
Cyclic presentations of groups, knot groups, LOG groups, and 3-dimensional manifolds
Abstract: A cyclic presentation of a group is a group presentation with an equal number of generators and defining relations that admits a cyclic symmetry; the group it defines is called a cyclically presented group. Prominent examples include Fibonacci groups and Sieradski groups. Many 3-dimensional manifolds, such as the Brieskorn manifolds have cyclically presented fundamental group.
Labelled Oriented Graph (LOG) groups are a wide class of groups that contains all knot and link groups, high dimensional knot groups, and Artin's braid groups. They are defined in terms of a Wirtinger-like presentation formed from the LOG.
The abelianisation (the largest commutative quotient) of a cyclically presented group is determined by the Smith Normal form of a circulant matrix associated to the presentation. In an ongoing programme of research with Noferini we develop tools for calculating these Smith forms. In this talk I will discuss some of these results and how they can be used to classify cyclically presented groups that are LOG groups and to calculate the homology of the 3-dimensional Brieskorn manifolds.
The webpage of the seminar is at
math.aalto.fi/en/research/discrete/seminars/agc/<https://math.aalto.fi/en/research/discrete/seminars/agc/>
and we have a mailing list at
https://list.aalto.fi/mailman/listinfo/agc-math-aalto

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