LisMath Seminar 

24/06/2020, 17:00 — 18:00 — Online
António Lages, LisMath, Instituto Superior Técnico, Universidade de Lisboa

From racks to pointed Hopf algebras

A quandle is a group-like algebraic structure whose axioms reflect the Reidemeister moves from Knot Theory [2]. This means that quandles naturally give rise to knot invariants, which can be efficiently used in distinguishing knots. Therefore, we expect that even a partial classification of quandles will improve knot detection and distinction techniques. In [1], several important steps are made towards a complete classification of quandles. In this talk, after properly introducing Knot Theory, we present some of these results along with examples and applications.

Bibliography:

[1] N. Andruskiewitsch and M. Graña, From racks to pointed Hopf algebras, Adv. Math. 178 (2003) 177-243

[2] D. Joyce, A classifying invariant of knots, the knot quandle, J. Pure Appl. Alg. 23 (1982), 37-65

See also

lismath_seminar_antonio_lages.pdf