相关论文: Factorizations of diffeomorphisms of compact surfa…
We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight…
We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular,…
We generalize a classical result concerning smooth germs of surfaces, by proving that monodromies on links of isolated complex surface singularities associated with reduced holomorphic map germs admit a positive factorization. As a…
We present relations in the mapping class monoid of $S_{0,0}^n$ between products of boundary parallel twists and those involving only non boundary parallel twists. These are of particular interest because each element gives an open book…
A result of Honda, Kazez, and Mati\'{c} states that a contact structure is tight if and only if all its supporting open books are right-veering. We show a combinatorial way of detecting the left-veering arcs in open books, implying the…
We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of $\B^4$ whose branch set is a positive braided surface. As a consequence, we have that a smooth oriented…
On a compact oriented surface of genus $g$ with $n\geq 1$ boundary components, $\delta_1, \delta_2,\ldots, \delta_n$, we consider positive factorizations of the boundary multitwist $t_{\delta_1} t_{\delta_2} \cdots t_{\delta_n}$, where…
For an open book decomposition $(S,\phi)$, the fractional Dehn twist coefficients are rational numbers measuring the amount that the monodromy $\phi$ twists the surface $S$ near each boundary component. In general, the twist coefficients do…
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…
Extending the notion of monodromies associated with open books of $3$-manifolds, we consider monodromies for all incompressible surfaces in $3$-manifolds as partial self-maps of the arc set of the surfaces. We use them to develop a…
Ruberman gave the first examples of self-diffeomorphisms of four-manifolds that are isotopic to the identity in the topological category but not smoothly so. We give another example of this phenomenon, using the Dehn twist along a 3-sphere…
Given a 3-holed sphere decomposition of an orientable closed surface, it is shown that each orientation preserving homeomorphism of the surface is isotopic to a composition AB where A is a product of positive Dehn twists and B is a product…
We introduce an essential open book foliation, a refinement of the open book foliation, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as…
We describe the compact Lorentzian $3$-manifolds admitting a parallel lightlike vector field. The classification of compact Lorentzian $3$-manifolds admitting non-isometric affine diffeomorphisms follows, together with the complete…
Let $X$ be a compact orientable non-Haken 3-manifold modeled on the Thurston geometry $\text{Nil}$. We show that the diffeomorphism group $\text{Diff}(X)$ deformation retracts to the isometry group $\text{Isom}(X)$. Combining this with…
Suppose S is a compact surface with boundary, and let g be a diffeomorphism of S which fixes the boundary pointwise. We denote by (M_{S,g},\xi_{S,g})$ the contact 3-manifold compatible with the open book (S,g). In this article, we construct…
A branched affine structure on a compact topological surface with marked points is a complex affine structure outside the marked points. We give a proof of an unpublished foundational theorem of Veech, stating that any branched affine…
We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.
A homeomorphism of a 3-manifold M is said to be Dehn twists on the boundary when its restriction to the boundary of M is isotopic to the identity on the complement of a collection of disjoint simple closed curves in the boundary of M. In…
We investigate two specific contractible manifolds (one Stein, and the other non-Stein) whose boundaries have non-trivial mapping class groups. In both cases we show that every diffeomorphism of their boundary extends to a diffeomorphism of…