Series of colloquia by PhD students to PhD students!
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For any inquiries (or if you want to partecipate with your own talk), you can write to luigi [dot] defilpo [at] uniroma1 [dot] it
Tuesday, May 19th - 14:00-15:30 Aula F
Braids, pure braids, and bonded braids
Apart from the classic hairstyle, braids are also mathematical objects, reminiscent of permutations but with the additional information of which object passes “in front” of the other in every transposition. Of course they can be represented by the intertwining of strands in the plane, or what naively is a braid.
Various derivations of braids have been introduced in mathematics, such as virtual braids, singular braids, and last but not least bonded braids. These happen when two strands of a braid are tied together with an arc, called bond. Bonded braids are related to other braided structures, such as pure braids, braids associated to the trivial permutation.
Pure braids are dangerous objects in braid groups. Artin himself recommended to never comb your pure braids unsupervised. We will approach them with caution, as they represent a suitable model for bonded braids and can tell us more about them in a familiar context.