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Knot concordances and alternating knots

- Stefan Friedl, C. Livingston, Raphael Zentner
- Mathematics
- 28 December 2015

There is an infinitely generated free subgroup of the smooth knot concordance group with the property that no nontrivial element in this subgroup can be represented by an alternating knot. This… Expand

8 1- PDF

Representation spaces of pretzel knots

- Raphael Zentner
- Mathematics
- 13 December 2010

We study the representation spaces $R(K;\bf{i})$ as appearing in Kronheimer and Mrowka's framed instanton knot Floer homology, for a class of pretzel knots. In particular, for pretzel knots… Expand

8 1- PDF

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

- Raphael Zentner
- Mathematics
- 11 January 2015

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… Expand

10 1- PDF

The quantum sl(n) graph invariant and a moduli space

- Andrew Lobb, Raphael Zentner
- Mathematics
- 24 April 2012

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… Expand

7 1- PDF

Integer homology $3$-spheres admit irreducible representations in $\operatorname{SL}(2,\mathbb{C})$

- Raphael Zentner
- Mathematics
- 27 May 2016

We prove that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL(2,C). For hyperbolic integer… Expand

16- PDF

Khovanov width and dealternation number of positive braid links.

- S. Baader, P. Feller, Lukas Lewark, Raphael Zentner
- Mathematics
- 14 October 2016

We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic technique, combined… Expand

3- PDF

Alternating numbers of torus knots with small braid index

- P. Feller, S. Pohlmann, Raphael Zentner
- Mathematics
- 24 August 2015

We calculate the alternating number of torus knots with braid index 4 and less. For the lower bound, we use the upsilon-invariant recently introduced by Ozsv\'ath, Stipsicz, and Szab\'o. For the… Expand

4- PDF

ON LOGARITHMIC TRANSFORMATIONS ON THE HOPF SURFACE

- Raphael Zentner
- 2008

In this note we study logarithmic transformations in the sense of differential topology on two fibers of the Hopf surface. It is known that such transformations are susceptible to yield exotic smooth… Expand

Toroidal homology spheres and SU(2)-representations

- Tye Lidman, Juanita Pinz'on-Caicedo, Raphael Zentner
- Mathematics
- 7 January 2021

We prove that if an integer homology three-sphere contains an embedded incompressible torus, then its fundamental group admits irreducible SU(2)representations. Our methods use instanton Floer… Expand

1- PDF

$PU(N)$ monopoles, higher rank instantons, and the monopole invariants

- Raphael Zentner
- Mathematics
- 29 February 2008

A famous conjecture in gauge theory mathematics, attributed to Witten, suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying… Expand

1- PDF

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