Raphael Zentner

Representation spaces of pretzel knots

We study the representation spaces

The Quantum sl(N) Graph Invariant and a Moduli Space

R(K;\bf{i})

A class of knots with simple SU(2)-representations

as appearing in Kronheimer and Mrowkas framed instanton knot Floer homology, for a class of pretzel knots. In particular, for pretzel knots

A vanishing result for a Casson-type instanton invariant

P(p,q,r)

The influence of varus and valgus deviation on patellar kinematics in healthy knees: An exploratory cadaver study

with

Alternating numbers of torus knots with small braid index

p, q, r

On spectral sequences from Khovanov homology

pairwise coprime, these appear to be non-degenerate and comprise representations in SU(2) that are not binary dihedral.

Knot concordances and alternating knots

We associate a moduli problem to a colored trivalent graph; such graphs, when planar, appear in the state-sum description of the quantum sl(N) knot polynomial due to Murakami, Ohtsuki, and Yamada. We discuss how the resulting moduli space can be thought of a representation variety. We show that the Euler characteristic of the moduli space is equal to the quantum sl(N) polynomial of the graph evaluated at unity. Possible extensions of the result are also indicated.

Khovanov width and dealternation number of positive braid links

We call a knot in the 3-sphere SU(2)-simple if all representations of the fundamental group of its complement which map a meridian to a trace-free element in SU(2) are binary dihedral. This is a generalization of being a 2-bridge knot. Pretzel knots with bridge number