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Isacco Nonino

Publications and source records attributed to Isacco Nonino.

10 recordsLinked to original sources
arXiv2026

Khovanov monodromy groups via motions

For any link, we define a monodromy map from the motion group of the link to the group of automorphisms of the link's Khovanov homology. The image of this map is the \emph{unoriented monodromy group} of the link. This map allows us to convert results concerning motion groups of links into ones about their Khovanov monodromy. In particular, we use a characterisation of the motion groups of split links to write their unoriented monodromy groups as an explicit semidirect product in terms of their unsplit pieces. We give some demonstrative examples, computing the unoriented monodromy groups of unlinks, Hopf links, and split links composed of pieces thereof.

math.GT↗
arXiv2026

A survey on mapping class groups of 3-manifolds

We survey computations and tools concerning the mapping class group of a compact, oriented, connected 3-manifold $M$. We provide a guide to the literature and sketch proofs for various families of irreducible and geometric 3-manifolds. We also consider JSJ and prime decompositions of 3-manifolds, and consequences for their mapping class groups.

math.GT↗
arXiv2026

Transverse knots determined by their cyclic branched covers

Harvey-Kawamuro-Plamenevskaya demonstrated the existence of (transversely) non-isotopic transverse knots such that for every $n>1$ their $n$-fold cyclic branched covers are contactomorphic. In this short note, we construct other examples of non-isotopic transverse knots that have contactomorphic cyclic branched covers. Conversely, we prove that the transverse isotopy classes of many transverse knots are actually determined by the contactomorphism type of their cyclic branched covers.

math.GT↗
arXiv2025

Contact surgery distance

In this article, we define the contact surgery distance of two contact 3-manifolds $(M,ξ)$ and $(M',ξ')$ as the minimal number of contact surgeries needed to obtain $(M,ξ)$ from $(M',ξ')$. Our main result states that the contact surgery distance between two contact $3$-manifolds is at most $5$ larger than the topological surgery distance between the underlying smooth manifolds. As a byproduct of our proof, we classify the rational homology $3$-spheres on which the $d_3$-invariant of a $2$-plane field already determines its $Γ$-invariant and Euler class.

math.GT↗
arXiv2025

Non-fibered strongly quasipositive links and tightness

It is well known that for fibered links in $\mathbb{S}^3$ being strongly quasipositive and supporting a tight contact structure are equivalent notions (arXiv:math/0509499). In this note we analyze the relation between these two properties for non fibered links. A non fibered link (together with an incompressible Seifert surface) induces a natural partial open book (arXiv:2509.09615). We prove that strongly quasipositive links induce tight contact structures. We also show that, in contrast to the fibered case, the converse is not true, giving examples of links that are not strongly quasipositive but support tight contact structures.

math.GT↗
arXiv2025

Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds

We define obstructions which obstruct topological pseudo-isotopies from being isotopic to isotopies in dimension four. These match the smooth obstructions of Hatcher-Wagoner for smooth pseudo-isotopies, and accordingly are valued in certain Whitehead groups. We show that our obstructions are fully realisable, and we use these realisations to build homeomorphisms of $Y\times S^1$ for many 3-manifolds $Y$ that are pseudo-isotopic to the identity but not isotopic to the identity.

math.GT↗
arXiv2024

Diffeotopy groups of non-compact 4-manifolds

We provide information on diffeotopy groups of exotic smoothings of punctured 4-manifolds, extending previous results on diffeotopy groups of exotic $\mathbb{R}^4$'s. In particular, we prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there are uncountably many distinct smoothings of $M\smallsetminus S$ whose diffeotopy groups are uncountable. We then prove that for a smoothable 4-manifold $M$ and for a non-empty, discrete set of points $S \subsetneq \mathring{M}$, there exists a smoothing of $M\smallsetminus S$ whose diffeotopy groups have similar properties as $\mathcal{R}_U$, Freedman and Taylor's universal $\mathbb{R}^4$. Moreover, we prove that if $M$ is non-smoothable, both results still hold under the assumption that $|S| \ge 2$.

math.GT↗
arXiv2024

$L$-space knots with positive surgeries that are not weakly symplectically fillable

In this paper we discuss a general strategy to detect the absence of weakly symplectic fillings of $L$-spaces. We start from a generic $L$-space knot and consider (positive) Dehn surgeries on it. We compute, using arithmetic data depending only on the knot type and the surgery coefficient, the value of the relevant geometric invariants used to obstruct fillability. We also provide a new example of an infinite family of hyperbolic $L$-spaces that do not admit weakly symplectic fillings. These are manifolds that lie inside $\{\text{Tight}\}$ but not inside $\{\text{Weakly Fillable}\}$.

math.GT↗
arXiv2023

Tight contact structures on a family of hyperbolic L-spaces

We classify tight contact structures on various surgeries on the Whitehead link, which provides the first classification result on an infinite family of hyperbolic L-spaces. We also determine which of the tight contact structures are Stein fillable and which are virtually overtwisted.

math.GT↗