Molecular braids in a nutshell
A braid on n-strands is an intertwining of the strands starting from ’top’ to ’bot- tom’ such that the strands don’t turn back up. Mathematically, these objects are known as Artin’s braid group on n-strands and can be formalised in three distinct ways, via configuration spaces, via generators and relations and as mapping class groups. The first half of the talk will focus on a quick review on the theory of braid groups. The second half will focus on a particular class of braids we call as ’Special Diagonal Braids’ (suggestions for better names are welcome!). This class is motivated from topological isomers in coordination polymers in chemistry that are characterised by weaving. Their 1-dimensional interwoven structures can be mathematically described as braids. We aim to model actual realisations of topological braids in Euclidean 3- space by such molecules, their embeddings and co-ordinates. We will discuss their properties, their so-called linking graphs and some open problems.