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        Questions tagged [sg.symplectic-geometry]

        Hamiltonian systems, symplectic flows, classical integrable systems

        6
        votes
        1answer
        171 views

        Strip breaking phenomenon in the Gromov compactification of Moduli space of Pseudoholomorphic curves

        As the title suggests, I want to understand the strip breaking phenomenon that happens when I Gromov-compactify the moduli space of pseudoholomorphic curves from the holomorphic strip $\Bbb R \times [...
        7
        votes
        2answers
        294 views

        Volume of manifolds embedded in $\mathbb{R}^n$

        Let $N$ be a closed, connected, oriented hypersurface of $\mathbb{R}^n$. Such a manifold inherits a volume form from the usual volume from on $\mathbb{R}^n$ and has an associated volume given by ...
        8
        votes
        1answer
        295 views

        Constants of motion for Droop equation

        There is an important ODE system in biochemistry, Droop's equations: $$s'=1-s-\frac{sx}{a_1+s}$$ $$x'=a_2\big(1-\frac{1}{q}\big)x-x$$ $$q'=\frac{a_3s}{a_1+s}-a_2(q-1)$$ Relatively easy one finds a ...
        3
        votes
        0answers
        51 views

        Symplectic vector fields everywhere transverse to a co-dimension one hypersurface

        Usually when speaking about vector fields transverse to a hypersurface in a symplectic manifold, we talk about Liouville vector fields, i.e. vector fields $X$ with the property that $\mathcal{L}_X\...
        4
        votes
        0answers
        66 views

        Lagrangian subgroup of a nonabelian Lie group

        My post here concerns the concept of Lagrangian subgroup for a non-abelian Lie group, such as a semi-simple non-abelian Lie group for gauge theory. See a previous post for other background ...
        1
        vote
        1answer
        159 views

        Floer equation and Cauchy Riemann equation

        Consider a symplectic manifold $(M,\omega)$ with the property that $\pi_2(M) = 0$. Given a time dependent hamiltonian $H_t$ on $M$, and a $\omega$-compatible almost complex structure J on M, we may ...
        2
        votes
        0answers
        86 views

        Limitations of the splitting construction and SFT

        I am trying to understand the so-called symplectic field theory (SFT) machinery used in symplectic topology. As I understand it, one of the applications of SFT (or rather, of the splitting ...
        2
        votes
        0answers
        61 views

        Transitivity of Diff on the space of embeddings of balls

        Given 2 symplectic embeddings $g_0$ and $g_1$ of a 4-ball of radius $r \leq 1$ into the 4-ball of radius 1 (all equipped with the standard symplectic form coming from $\mathbb{R}^4$), does there exist ...
        3
        votes
        0answers
        74 views

        Large isometry groups of Kaehler manifolds

        Let $M$ be a closed simply-connected Kaehler manifold that is not isomorphic to a product of lower-dimensional Kaehler manifolds. Pick an orientation for $\mathbb{C}$; this endows $M$ with an ...
        4
        votes
        0answers
        66 views

        Pairs of J-holomorphic curves

        Let $(M, \omega)$ be a symplectic 4-manifold and let $A$ and $B$ be symplectic submanifolds on M such that $A \cap B = p \in M$.Under what conditions can I find a $\omega$-compatible almost complex ...
        3
        votes
        0answers
        108 views

        An inequality for symplectic manifolds

        Question: Is there a closed symplectic manifold satisfying the following? $$|Td(M)| > \sum_{i \in \mathbb{Z}} b_{i}(M) $$ here $Td(X)$ is the Todd genus of $M$ i.e. the integral of the Todd class ...
        3
        votes
        0answers
        101 views

        Symplectic Chern class of holomorphic symplectic manifold

        I've posted this question already on math.stackexchage. Unfortunately, it did not receive any answers even though there was a bounty on it. So maybe somebody of you could help me. I apologize if this ...
        4
        votes
        0answers
        106 views

        Diffeomorphism of $ \mathbb{C}P^2 \# ~\overline{\mathbb{C}P^2}$

        I am currently reading Dusa McDuff's paper "Blow ups and symplectic embedding in dimension 4" and had a few questions regarding the paper. In the paper McDuff uses the following notation. $X = \...
        5
        votes
        1answer
        179 views

        Multiple mirrors phenomenon from SYZ and HMS perspective

        There is a set of ideas called mirror symmetry which, roughly speaking, relates symplectic and complex geometry of Calabi--Yau manifolds. There are also extensions to Fano and general type varieties ...
        4
        votes
        1answer
        498 views

        The singular cohomology embeds into the symplectic cohomology

        Viterbo's theorem on cotangent bundles $M=T^*N$ tells you in particular that singular cohomology $H^*(M)$ gets embedded in $SH^*(M)$ via the $c^*$ map. Having a Weinstein manifold (or more generally ...

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