4,899 research outputs found
Duality for Legendrian contact homology
The main result of this paper is that, off of a `fundamental class' in degree
1, the linearized Legendrian contact homology obeys a version of Poincare
duality between homology groups in degrees k and -k. Not only does the result
itself simplify calculations, but its proof also establishes a framework for
analyzing cohomology operations on the linearized Legendrian contact homology.Comment: This is the version published by Geometry & Topology on 8 December
200
A Duality Exact Sequence for Legendrian Contact Homology
We establish a long exact sequence for Legendrian submanifolds L in P x R,
where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that
displaces the projection of L off of itself. In this sequence, the singular
homology H_* maps to linearized contact cohomology CH^* which maps to
linearized contact homology CH_* which maps to singular homology. In
particular, the sequence implies a duality between the kernel of the map
(CH_*\to H_*) and the cokernel of the map (H_* \to CH^*). Furthermore, this
duality is compatible with Poincare duality in L in the following sense: the
Poincare dual of a singular class which is the image of a in CH_* maps to a
class \alpha in CH^* such that \alpha(a)=1.
The exact sequence generalizes the duality for Legendrian knots in Euclidean
3-space [24] and leads to a refinement of the Arnold Conjecture for double
points of an exact Lagrangian admitting a Legendrian lift with linearizable
contact homology, first proved in [6].Comment: 57 pages, 10 figures. Improved exposition and expanded analytic
detai
Trisecting non-Lagrangian theories
We propose a way to define and compute invariants of general smooth
4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3
theories in which the problem is reduced to a fairly standard computation in
topological A-model, albeit with rather unusual targets, such as compact and
non-compact Gepner models, asymmetric orbifolds, N=(2,2) linear dilaton
theories, "self-mirror" geometries, varieties with complex multiplication, etc.Comment: 49 pages, 8 figures, 8 tables, v2: a reference adde
Holographic Entanglement Entropy of Anisotropic Minimal Surfaces in LLM Geometries
We calculate the holographic entanglement entropy (HEE) of the
orbifold of Lin-Lunin-Maldacena (LLM) geometries which are dual to the vacua of
the mass-deformed ABJM theory with Chern-Simons level . By solving the
partial differential equations analytically, we obtain the HEEs for all LLM
solutions with arbitrary M2 charge and up to -order where
is the mass parameter. The renormalized entanglement entropies are all
monotonically decreasing near the UV fixed point in accordance with the
-theorem. Except the multiplication factor and to all orders in ,
they are independent of the overall scaling of Young diagrams which
characterize LLM geometries. Therefore we can classify the HEEs of LLM
geometries with orbifold in terms of the shape of Young diagrams
modulo overall size. HEE of each family is a pure number independent of the 't
Hooft coupling constant except the overall multiplication factor. We extend our
analysis to obtain HEE analytically to -order for the symmetric
droplet case.Comment: 15 pages, 1 figur
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