اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSquared Dehn twists and deformed symplectic invariants
178
0
0.0
(
0
)
تأليف
Kyler Siegel
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We establish an infinitesimal version of fragility for squared Dehn twists around even dimensional Lagrangian spheres. The precise formulation involves twisting the Fukaya category by a closed two-form or bulk deforming it by a half-dimensional cycle. As our main application, we compute the twisted and bulk deformed symplectic cohomology of the subflexible Weinstein manifolds constructed in cite{murphysiegel}.
قيم البحث
اقرأ أيضاً
In this paper we introduce the following new ingredients: (1) rework on part of the Lagrangian surgery theory; (2) constructions of Lagrangian cobordisms on product symplectic manifolds; (3) extending Biran-Cornea Lagrangian cobordism theory to the i
mmersed category. As a result, we manifest Seidels exact sequences (both the Lagrangian version and the symplectomorphism version), as well as Wehrheim-Woodwards family Dehn twist sequence (including the codimension-1 case missing in the literature) as consequences of our surgery/cobordism constructions. Moreover, we obtain an expression of the autoequivalence of Fukaya category induced by Dehn twists along Lagrangian $mathbb{RP}^n$, $mathbb{CP}^n$ and $mathbb{HP}^n$, which matches Huybrechts-Thomass mirror prediction of the $mathbb{CP}^n$ case modulo connecting maps. We also prove the split generation of any symplectomorphism by Dehn twists in $ADE$-type Milnor fibers.
We introduce new invariants associated to collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these invariants invo
lves various flavors of Floer theory. We present applications to approximation theory on symplectic manifolds and to Hamiltonian dynamics.
We give detailed descriptions of gluing pseudoholomorphic maps in symplectic geometry, especially in the presence of an obstruction bundle. The main motivation is to try to compare the symplectic and enumerative invariants of algebraic manifolds. The
se descriptions can also be used to enumerate rational curves with high-order degeneracies of local nature in projective spaces.
A textit{multicurve} $C$ on a closed orientable surface is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. The Dehn twist $t_{C}$ about $C$ is the product of the Dehn twists about the individual curves. In t
his paper, we give necessary and sufficient conditions for the existence of a root of such a Dehn twist, that is, a homeomorphism $h$ such that $h^n = t_{C}$. We give combinatorial data that corresponds to such roots, and use it to determine upper bounds for $n$. Finally, we classify all such roots up to conjugacy for surfaces of genus 3 and 4.
Let $text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g geq 1$. In this paper, we develop various methods for factoring periodic mapping classes into Dehn twists, up to conjugacy. As applications, we develop
methods for factoring certain roots of Dehn twists as words in Dehn twists. We will also show the existence of conjugates of periodic maps of order $4g$ and $4g+2$, for $ggeq 2$, whose product is pseudo-Anosov.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
