Related papers: Positive Dehn Twist Expressions for some New Invol…
The positive Dehn twist expressions for the generalizations of the new involutions described in math.GT/0404310 are presented. The homeomorphism types of the Lefschetz fibrations that they define are determined for several examples.
Positive Dehn twist products for some elements of finite order in the mapping class group of a 2-dimensional closed, compact, oriented surface $\Sigma_g$, which are rotations of $\Sigma_g$ through $2\pi /p$, are presented. The homeomorphism…
We construct a relation among right-handed Dehn twists in the mapping class group of a compact oriented surface of genus g with 4g+4 boundary components. This relation gives an explicit topological description of 4g+4 disjoint (-1)-sections…
The purpose of this note is to explain a combinatorial description of closed smooth oriented 4-manifolds in terms of positive Dehn twist factorizations of surface mapping classes, and further explore these connections. This is obtained via…
In this article, we study the maximal length of positive Dehn twist factorizations of surface mapping classes. In connection to fundamental questions regarding the uniform topology of symplectic 4-manifolds and Stein fillings of contact…
In the symplectic mapping class group of a $4$-dimensional Weinstein domain, we give a relation between two products of (right-handed) Dehn twists via holomorphic curve techniques. A key ingredient of the construction is a solution to the…
We describe symplectic mapping class relations between products of positive Dehn twists along Lagrangian spheres in Weinstein $4$-manifolds, all of which are affine $\mathbb{C}$ varieties. The relations are obtained by applying…
Integral symplectic 4-manifolds may be described in terms of Lefschetz fibrations. In this note we give a formula for the signature of any Lefschetz fibration in terms of the second cohomology of the moduli space of stable curves. As a…
In this paper we give an explicit construction of a symplectic Lefschetz fibration whose total space is a smooth compact four dimensional manifold with a prescribed fundamental group. We also study the numerical properties of the sections…
A complete description of the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4 is given. As a by-product we get a positive relation among right hand Dehn twists in the mapping class group of a closed…
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 a connection between the lantern relation in mapping class groups and the rational blowing down process for 4-manifolds. More precisely, if we change a positive relator in Dehn twist generators of the mapping class group by using…
We find a new relation among right-handed Dehn twists in the mapping class group of a $k$-holed torus for $4 \leq k \leq 9$. This relation induces an elliptic Lefschetz pencil structure on the four-manifold \cp $#(9-k)$ \cpb $ $ with $k$…
This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological…
In this paper, we examine mapping class group relations of some symplectic manifolds. For each $n\geq 1$ and $k \geq 1$, we show that the $2n$-dimensional Weinstein domain $W = \{f=\delta\} \cap B^{2n+2}$, determined by the degree $k$…
We develop techniques to construct explicit symplectic Lefschetz fibrations over the 2-sphere with any prescribed signature and any spin type when the signature is divisible by 16. This solves a long-standing conjecture on the existence of…
We establish constraints on the topology of smooth Lefschetz fibrations with $4$-dimensional fibers, by studying the family Bauer-Furuta invariant. To compute this invariant, we analyze the framed bordism class of 1-dimensional…
Let M be a smooth 4-manifold which admits a genus g Lefschetz fibration over D^2 or S^2. We develop a technique to compute the signature of M using the global monodromy of this fibration.
A positive Dehn twist product for a $\mathbb{Z}_3$ action with $g+2$ fixed points on the 2-dimensional closed, compact, oriented surface $\Sigma_g$ is presented. The homeomorphism invariants of the resulting symplectic 4-manifolds are…
We initiate a study of positive multisections of Lefschetz fibrations via positive factorizations in framed mapping class groups of surfaces. Using our methods, one can effectively capture various interesting symplectic surfaces in…