Some Notions of Simplicity in 3-dimensions Seminar
- Time:
- 15:00 - 16:00
- Date:
- 27 January 2017
- Venue:
- Ketley Room, Room 4001, Building 54, Mathematical Sciences, University of Southampton, Highfield, Southampton, SO17 1BJ
For more information regarding this seminar, please telephone Dr Jan Spakula on 023 8059 3137 or email Jan.Spakula@southampton.ac.uk .
Event details
The aim of this talk is to describe some aspects of a still-developing story in low-dimensional topology, namely, the conjectural relationship between left-orderable groups, foliations, and Floer homology. Much of the focus will be on introducing (and motivating the study of) these seemingly disparate different objects.
Speaker information
Dr Liam Watson , University of Glasgow. His area of research is low-dimensional topology. He is interested in Khovanov homology and Heegaard Floer homology, and his work is informed by connections between these two theories. To date, this has fallen along two distinct but, as it happens, quite interconnected lines of inquiry: Symmetries and Khovanov homology The relationship between Khovanov homology and Heegaard Floer homology by way of double branched covers suggests where to look for new applications in Khovanov homology. This seems to strengthen the connection between the two theories and gives rise, for example, to an algebraic tool for studying the mapping class group of the knot complement (also known as the knot's symmetry group). L-spaces and left-orderability The simplest three-manifolds, from the vantage point of Heegaard Floer theory, are L-spaces. These come up in application and satisfy interesting properties, but a complete understanding of L-spaces is lacking. However, there appear to be strong connections with foliations and left-orderable groups.