Page 588 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 588
LOW-DIMENSIONAL TOPOLOGY (MS-11)
Combinatorial cusp counting in curves
Sebastian Baader, sebastian.baader@math.unibe.ch
University Bern, Switzerland
A classic open problem in algebraic geometry asks for the maximal number of cusps in plane
algebraic curves of degree d. This is closely related to determining the minimal genus of smooth
cobordisms between torus links and connected sums of trefoil knots. As we will see, the signa-
ture function is strikingly effective at estimating the latter.
Exotic 4-manifolds with signature zero
Inanc Baykur, baykur@math.umass.edu
University of Massachusetts Amherst, United States
We will talk about our recent construction of the smallest closed exotic 4-manifolds with sig-
nature zero known to date. Our novel examples are derived from fairly special small Lefschetz
fibrations we build, with spin and non-spin monodromies. This is joint work with N. Hamada.
Quasi-morphisms on Surface Diffeomorphism Groups
Jonathan Bowden, jpbowden1981@yahoo.com.au
University of Regensburg, Germany
Coauthors: Sebastian Hensel, Richard Webb
We show that the identity component of the group of diffeomorphisms of a closed oriented
surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also
deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, an-
swering a question of Burago–Ivanov–Polterovich. As a key tool we construct a hyperbolic
graph on which these groups act, which is the analog of the curve graph for the mapping class
group. (joint with S. Hensel and R. Webb)
L-space links and link Floer homology
Alberto Cavallo, cavallo@mpim-bonn.mpg.de
Max Planck Institute for Mathematics, Germany
It is a standard result in knot Floer homology that L-space knots are fibered and strongly quasi-
positive. The same does not hold for L-space links; in fact, we can provide examples of L-space
links where neither of the two properties hold.
In a work joint with Beibei Liu, we show that if a restriction is put on the family of L-space
links then we can prove exactly the same result. Namely, we consider only the ones for which
the H-function, a concordance invariant from the link Floer homology group, has a specific
shape.
The goal of this talk is to present a proof of the mentioned statement. This will be done
by using the τ -set of a link and the fact that it characterizes fibered and strongly quasi positive
links in S3.
586
Combinatorial cusp counting in curves
Sebastian Baader, sebastian.baader@math.unibe.ch
University Bern, Switzerland
A classic open problem in algebraic geometry asks for the maximal number of cusps in plane
algebraic curves of degree d. This is closely related to determining the minimal genus of smooth
cobordisms between torus links and connected sums of trefoil knots. As we will see, the signa-
ture function is strikingly effective at estimating the latter.
Exotic 4-manifolds with signature zero
Inanc Baykur, baykur@math.umass.edu
University of Massachusetts Amherst, United States
We will talk about our recent construction of the smallest closed exotic 4-manifolds with sig-
nature zero known to date. Our novel examples are derived from fairly special small Lefschetz
fibrations we build, with spin and non-spin monodromies. This is joint work with N. Hamada.
Quasi-morphisms on Surface Diffeomorphism Groups
Jonathan Bowden, jpbowden1981@yahoo.com.au
University of Regensburg, Germany
Coauthors: Sebastian Hensel, Richard Webb
We show that the identity component of the group of diffeomorphisms of a closed oriented
surface of positive genus admits many unbounded quasi-morphisms. As a corollary, we also
deduce that this group is not uniformly perfect and its fragmentation norm is unbounded, an-
swering a question of Burago–Ivanov–Polterovich. As a key tool we construct a hyperbolic
graph on which these groups act, which is the analog of the curve graph for the mapping class
group. (joint with S. Hensel and R. Webb)
L-space links and link Floer homology
Alberto Cavallo, cavallo@mpim-bonn.mpg.de
Max Planck Institute for Mathematics, Germany
It is a standard result in knot Floer homology that L-space knots are fibered and strongly quasi-
positive. The same does not hold for L-space links; in fact, we can provide examples of L-space
links where neither of the two properties hold.
In a work joint with Beibei Liu, we show that if a restriction is put on the family of L-space
links then we can prove exactly the same result. Namely, we consider only the ones for which
the H-function, a concordance invariant from the link Floer homology group, has a specific
shape.
The goal of this talk is to present a proof of the mentioned statement. This will be done
by using the τ -set of a link and the fact that it characterizes fibered and strongly quasi positive
links in S3.
586
