Page 590 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 590
LOW-DIMENSIONAL TOPOLOGY (MS-11)
Bonded knots: a topological model for knotted proteins
Boštjan Gabrovšek, bostjan.gabrovsek@fs.uni-lj.si
University of Ljubljana, Slovenia
We introduce bonded knots, oriented knots together with a set of properly embedded coloured
arcs. Such structures can be used to topologically model protein structures, where the knots cor-
respond to closed protein backbone chains and the bonds correspond to non-local interactions
between the amino acids. The bond colours encode the interaction type (disulphide bridges,
ionic bonds,...) that may appear in the conformation of the protein.
We will define the HOMFLYPT skein module of rigid and non-rigid coloured bonded knots
and show that the rigid version if freely generated by coloured Θ-curves and handcuff links,
whereas the non-rigid version is generated by trivial coloured Θ-curves. In other words, there
exits a well-defined invariant of rigid and non-rigid coloured bonded knots that respects the
HOMFLYPT skein relation.
Some 3-manifolds do not bound definite 4-manifolds
Marco Golla, marco.golla@univ-nantes.fr
CNRS, University of Nantes, France
Many construction of 3-manifolds automatically come with a 4-manifold with definite inter-
section form. Using Heegaard Floer correction terms and an analysis of short characteristic
covectors in bimodular lattices, we give an obstruction for a 3-manifold to bound a definite
4-manifold, and produce some concrete examples. This is joint work with Kyle Larson.
Flattening knotted surfaces
Eva Horvat, eva.horvat@pef.uni-lj.si
University of Ljubljana, Faculty for Education, Slovenia
A knotted surface K in the 4-sphere admits a projection to a 2-sphere, whose set of critical
points coincides with a hyperbolic diagram of K. We apply such projections, called flattenings,
to define three invariants of embedded surfaces: the width, the trunk and the partition number.
These invariants are studied for satellite 2-knots.
New Heegaard Floer slice genus and clasp number bounds
Andras Juhasz, juhasza@maths.ox.ac.uk
University of Oxford, United Kingdom
I will discuss several concordance invariants definted using knot Floer homology that give im-
provements over known slice genus and clasp number bounds from Heegaard Floer homology.
I also explain how the involutive correction terms of Hendricks and Manolescu give both a slice
genus and a clasp number bound. This is joint work with Ian Zemke.
588
Bonded knots: a topological model for knotted proteins
Boštjan Gabrovšek, bostjan.gabrovsek@fs.uni-lj.si
University of Ljubljana, Slovenia
We introduce bonded knots, oriented knots together with a set of properly embedded coloured
arcs. Such structures can be used to topologically model protein structures, where the knots cor-
respond to closed protein backbone chains and the bonds correspond to non-local interactions
between the amino acids. The bond colours encode the interaction type (disulphide bridges,
ionic bonds,...) that may appear in the conformation of the protein.
We will define the HOMFLYPT skein module of rigid and non-rigid coloured bonded knots
and show that the rigid version if freely generated by coloured Θ-curves and handcuff links,
whereas the non-rigid version is generated by trivial coloured Θ-curves. In other words, there
exits a well-defined invariant of rigid and non-rigid coloured bonded knots that respects the
HOMFLYPT skein relation.
Some 3-manifolds do not bound definite 4-manifolds
Marco Golla, marco.golla@univ-nantes.fr
CNRS, University of Nantes, France
Many construction of 3-manifolds automatically come with a 4-manifold with definite inter-
section form. Using Heegaard Floer correction terms and an analysis of short characteristic
covectors in bimodular lattices, we give an obstruction for a 3-manifold to bound a definite
4-manifold, and produce some concrete examples. This is joint work with Kyle Larson.
Flattening knotted surfaces
Eva Horvat, eva.horvat@pef.uni-lj.si
University of Ljubljana, Faculty for Education, Slovenia
A knotted surface K in the 4-sphere admits a projection to a 2-sphere, whose set of critical
points coincides with a hyperbolic diagram of K. We apply such projections, called flattenings,
to define three invariants of embedded surfaces: the width, the trunk and the partition number.
These invariants are studied for satellite 2-knots.
New Heegaard Floer slice genus and clasp number bounds
Andras Juhasz, juhasza@maths.ox.ac.uk
University of Oxford, United Kingdom
I will discuss several concordance invariants definted using knot Floer homology that give im-
provements over known slice genus and clasp number bounds from Heegaard Floer homology.
I also explain how the involutive correction terms of Hendricks and Manolescu give both a slice
genus and a clasp number bound. This is joint work with Ian Zemke.
588
