اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFibrancy of Symplectic Homology in Cotangent Bundles
161
0
0.0
(
0
)
تأليف
Thomas Kragh
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We describe how the result in [1] extends to prove the existence of a Serre type spectral sequence converging to the symplectic homology SH_*(M) of an exact Sub-Liouville domain M in a cotangent bundle T*N. We will define a notion of a fiber-wise symplectic homology SH_*(M,q) for each point q in N, which will define a graded local coefficient system on N. The spectral sequence will then have page two isomorphic to the homology of N with coefficients in this graded local system.
قيم البحث
اقرأ أيضاً
We prove a version of the Arnold conjecture for Lagrangian submanifolds of conformal symplectic manifolds: a Lagrangian $L$ which has non-zero Morse-Novikov homology for the restriction of the Lee form $beta$ cannot be disjoined from itself by a $C^0
$-small Hamiltonian isotopy. Furthermore for generic such isotopies the number of intersection points equals at least the sum of the free Betti numbers of the Morse-Novikov homology of $beta$. We also give a short exposition of conformal symplectic geometry, aimed at readers who are familiar with (standard) symplectic or contact geometry.
We classify symplectically foliated fillings of certain contact foliated manifolds. We show that up to symplectic deformation, the unique minimal symplectically foliated filling of the foliated sphere cotangent bundle of the Reeb foliation in the 3-s
phere is the associated disk cotangent bundle. En route to the proof, we study another foliated manifold, namely the product of a circle and an annulus with almost horizontal foliation. In this case, the foliated unit cotangent bundle does not have a unique minimal symplectic filling. We classify the foliated fillings of this manifold up to symplectic deformation equivalence using combinatorial invariants of the filling.
We use Menkes JSJ-type decomposition theorem for symplectic fillings to reduce the classification of strong and exact symplectic fillings of virtually overtwisted torus bundles to the same problem for tight lens spaces. For virtually overtwisted stru
ctures on elliptic or parabolic torus bundles, this gives a complete classification. For virtually overtwisted structures on hyperbolic torus bundles, we show that every strong or exact filling arises from a filling of a tight lens space via round symplectic 1-handle attachment, and we give a condition under which distinct tight lens space fillings yield the same torus bundle filling.
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.
Recently, Tsai-Tseng-Yau constructed new invariants of symplectic manifolds: a sequence of Aoo-algebras built of differential forms on the symplectic manifold. We show that these symplectic Aoo-algebras have a simple topological interpretation. Namel
y, when the cohomology class of the symplectic form is integral, these Aoo-algebras are equivalent to the standard de Rham differential graded algebra on certain odd-dimensional sphere bundles over the symplectic manifold. From this equivalence, we deduce for a closed symplectic manifold that Tsai-Tseng-Yaus symplectic Aoo-algebras satisfy the Calabi-Yau property, and importantly, that they can be used to define an intersection theory for coisotropic/isotropic chains. We further demonstrate that these symplectic Aoo-algebras satisfy several functorial properties and lay the groundwork for addressing Weinstein functoriality and invariance in the smooth category.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
