2,283 research outputs found
Exact Lagrangians in -surface singularities
In this paper we classify Lagrangian spheres in -surface singularities
up to Hamiltonian isotopy. Combining with a result of A. Ritter, this yields a
complete classification of exact Lagrangians in -surface singularities.Comment: Modified proof of Lemma 4.3 due to a simplification of relative
inflation from http://arxiv.org/abs/1305.0230. Expanded discussion on
ball-swapping, with an emphasis on the comparison with the algebro-geometric
point of view. Comments welcome
Equivariant split generation and mirror symmetry of special isogenous tori
We prove a version of equivariant split generation of Fukaya category when a
symplectic manifold admits a free action of a finite group . Combining this
with some generalizations of Seidel's algebraic frameworks from Seidel's book,
we obtain new cases of homological mirror symmetry for some symplectic tori
with non-split symplectic forms, which we call \textit{special isogenous tori}.
This extends the work of Abouzaid-Smith. We also show that derived Fukaya
categories are complete invariants of special isogenous tori.Comment: 42 page
Gauged Floer homology and spectral invariants
We define a version of spectral invariant in the vortex Floer theory for a
-Hamiltonian manifold . This defines potentially new (partial) symplectic
quasi-morphism and quasi-states when is not semi-positive. We also
establish a relation between vortex Hamiltonian Floer homology and Woodward's
quasimap Floer homology by constructing a closed-open string map between them.
This yields applications to study non-displaceability problems of subsets in
Comment: 48 pages. Comments welcome
Spherical twists and Lagrangian spherical manifolds
We study Dehn twists along Lagrangian submanifolds that are finite quotients
of spheres. We decribe the induced auto-equivalences to the derived Fukaya
category and explain its relation to twists along spherical functors.Comment: Comments are very welcome
Symplectormophism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians
We establish connections between contact isometry groups of certain contact
manifolds and compactly supported symplectomorphism groups of their
symplectizations. We apply these results to investigate the space of symplectic
embeddings of balls with a single conical singularity at the origin. Using
similar ideas, we also prove the longstanding expected result that the space of
Lagrangian \RR P^2 in T^*\RR P^2 is weakly contractible.Comment: 16 pages, 2 figures. Comments warmly welcome
Symplectic rational -surfaces and equivariant symplectic cones
We give characterizations of a finite group acting symplectically on a
rational surface ( blown up at two or more points). In
particular, we obtain a symplectic version of the dichotomy of -conic
bundles versus -del Pezzo surfaces for the corresponding -rational
surfaces, analogous to a classical result in algebraic geometry. Besides the
characterizations of the group (which is completely determined for the case
of , ), we also investigate
the equivariant symplectic minimality and equivariant symplectic cone of a
given -rational surface.Comment: 34 page
The symplectic mapping class group of \CC P^2 n{\bar{\CC P^2}} with
In this paper we prove that the Torelli part of the symplectomorphism groups
of the -point () blow-ups of the projective plane is trivial.
Consequently, we determine the symplectic mapping class group. It is generated
by reflections on spherical class with zero area
The Test of Topological Property of YbB6
Topological insulator is a recently discovered class of material with
topologically protected surface state. YbB6 is predicted to be moderately
correlated Z2 topological insulator similar to SmB6. Here, I experimentally
test the resistance property of bulk YbB6 to verify its topological property.
By changing the thickness of YbB6, I found out that although the data curves
did not completely conform to the theory of topology, the experimental
observation to the overall trend showed a similar topological phenomenon
Spherical Lagrangians via ball packings and symplectic cutting
In this paper we prove the connectedness of symplectic ball packings in the
complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that
are rational or ruled. Via a symplectic cutting construction this is a natural
extension of McDuff's connectedness of ball packings in other settings and this
result has applications to several different questions: smooth knotting and
unknottedness results for spherical Lagrangians, the transitivity of the action
of the symplectic Torelli group, classifying Lagrangian isotopy classes in the
presence of knotting, and detecting Floer-theoretically essential Lagrangian
tori in the del Pezzo surfaces.Comment: 25 pages, 2 figures; v2: minor corrections and clarifications, added
discussion after Corollary 1.2. To appear in Selecta Mathematic
Stability and Existence of Surfaces in Symplectic 4-Manifolds with
We establish various stability results for symplectic surfaces in symplectic
manifolds with . These results are then applied to prove the
existence of representatives of Lagrangian ADE-configurations as well as to
classify negative symplectic spheres in symplectic manifolds with
. This involves the explicit construction of spheres in
rational manifolds via a new construction technique called the tilted
transport.Comment: Comments welcome
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