Geometric Topology of Knots

Colored Turaev-Viro invariants for links in arbitrary 3-manifolds

speaker: Ekaterina Pervova (University of Pisa)

abstract: We consider certain invariants of links in 3-manifolds, obtained by a specialization of the Turaev-Viro invariants of 3-manifolds, that we call colored Turaev-Viro invariants. We analyze some basic properties of these invariants, including the behavior under connected sums of pairs away and along links. These properties allow us to provide examples of links in the three-dimensional sphere having the same HOMFLY polynomial and the same Kauffman polynomial but distinct Turaev-Viro invariants, and similar exam- ples for the Alexander polynomial. Finally, we establish a relation between the Turaev-Viro invariants of (M; L) and (the absolute value of) the Witten-Reshetikhin-Turaev invariants of (M; L'), where L' is L endowed with an arbitrary framing. (Joint with Carlo Petronio)

timetable:
Wed 25 May, 15:45 - 16:15, Aula Dini
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