Knots and Motives

Medientyp: E-Book; Video
Titel: Knots and Motives
Beteiligte: Horel, Geoffroy [Verfasser:in]; Asok, Aravind [Sonstige Person, Familie und Körperschaft]; Déglise, Frédéric [Sonstige Person, Familie und Körperschaft]; Garkusha, Grigory [Sonstige Person, Familie und Körperschaft]; Østvær, Paul Arne [Sonstige Person, Familie und Körperschaft]
Erschienen: [Erscheinungsort nicht ermittelbar]: Institut des Hautes Études Scientifiques (IHÉS), 2020
Erschienen in: Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory ; (Jan. 2020)
Umfang: 1 Online-Ressource (115 MB, 01:03:04:01)
Sprache: Englisch
DOI: 10.5446/50932
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Anmerkungen: Audiovisuelles Material
Beschreibung: The pure braid group is the fundamental group of the space of configurations of points in the complex plane. This topological space is the Betti realization of a scheme defined over the integers. It follows, by work initiated by Deligne and Goncharov, that the pronilpotent completion of the pure braid group is a motive over the integers (what this means precisely is that the Hopf algebra of functions on that group can be promoted to a Hopf algebra in an abelian category of motives over the integers). I will explain a partly conjectural extension of that story from braids to knots. The replacement of the lower central series of the pure braid group is the so-called Vassiliev filtration on knots. The proposed strategy to construct the desired motivic structure relies on the technology of manifold calculus of Goodwillie and Weiss
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