Related papers: Positive factorizations of mapping classes

We show that the morphisms from the braid group with n strands in the mapping class group of a surface with a possible non empty boundary, assuming that its genus is smaller or equal to n/2 are either cyclic morphisms (their images are…

We use slicing by nongeneric pencils of hypersurfaces and prove a new theorem of Lefschetz type for singular non compact spaces, at the homotopy level. As applications, we derive results on the topology of the fibres of polynomial functions…

For every integer g greater than or equal to 2, there exist infinitely many pairwise nonhomeomorphic smooth 4-manifolds that admit genus-g Lefschetz fibrations over S^2 but do not carry any complex structure with either orientation. This…

After reviewing recent results on symplectic Lefschetz pencils and symplectic branched covers of CP^2, we describe a new construction of maps from symplectic manifolds of any dimension to CP^2 and the associated monodromy invariants. We…

We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given g, we consider, for every $n\ge1$, a random quadrangulation $\mathfrak{q}_n$ uniformly distributed over the set of all rooted bipartite…

Let $(S,\mathfrak n)$ be a regular local ring and $f$ a non-zero element of $\mathfrak n^2$. A theorem due to Kn\"orrer states that there are finitely many isomorphism classes of maximal Cohen-Macaulay $R=S/(f)$-modules if and only if the…

In this article, we study the Euler class of taut foliations on the Dehn fillings of a $\mathbb{Q}$-homology solid torus. We give a necessary and sufficient condition for the Euler class of a foliation transverse to the core of the filling…

We prove that a Weinstein domain symplectically embedded in a closed symplectic manifold always admits symplectic hypersurfaces in its complement, possibly after a deformation. As a consequence, we obtain an obstruction for a closed…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

We consider finite-sheeted, regular, possibly branched covering spaces of compact surfaces with boundary and the associated liftable and symmetric mapping class groups. In particular, we classify when either of these subgroups coincides…

We characterize, for every higher smooth stack equipped with "tangential structure", the induced higher group extension of the geometric realization of its higher automorphism stack. We show that when restricted to smooth manifolds equipped…

We give a density condition for when, subject to a necessary parity condition, an eulerian graph or digraph may be cellularly embedded in an orientable surface so that it has exactly two faces, each bounded by an euler circuit, one of which…

In this article we study the problem of minimizing $a\chi+b\sigma$ on the class of all symplectic 4--manifolds with prescribed fundamental group $G$ ($\chi$ is the Euler characteristic, $\sigma$ is the signature, and $a,b\in \BR$), focusing…

Symplectic 4-manifolds $(X,\omega)$ with $b_+{=}1$ are roughly classified by the canonical class $K$ and the symplectic form $\omega$ depending upon the sign of $K^2$ and $K\cdot \omega$. Examples are known for each category except for the…

Margalit and Schleimer observed that Dehn twists on orientable surfaces have nontrivial roots. We investigate the problem of roots of a Dehn twist t_c about a nonseparating circle c in the mapping class group M(N_g) of a nonorientable…

Let X be a smooth, complex Fano variety, and delta(X) its Lefschetz defect. It is known that if delta(X) is at least 4, then X is isomorphic to a product SxT, where dim T=dim X-2. In this paper we prove a structure theorem for the case…

In this paper, we give some relations in the mapping class groups of oriented closed surfaces in the form that a product of a small number of right hand Dehn twists is equal to a single commutator. Consequently, we find upper bounds for the…

In the first part of this paper we prove that the mapping class subgroups generated by the $D$-th powers of Dehn twists (with $D\geq 2$) along a sparse collection of simple closed curves on an orientable surface are right angled Artin…

We prove that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology; in certain cases, we prove that all flexible fillings are symplectomorphic. As an application,…

In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic $d\delta$-lemma for any such foliations with the (transverse) $s$-Lefschetz property. As transversely…