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Myeonggi Kwon

Publications and source records attributed to Myeonggi Kwon.

16 recordsLinked to original sources
arXiv2026

Floer-theoretic entropy of exact symplectomorphisms

We introduce the notion of a Penner-type class of an exact symplectomorphism on a Liouville domain with an $A_k$-configuration of Lagrangian spheres for $k\geqslant 2$, and prove that such a class has positive Floer-theoretic entropy. As a corollary, we construct infinitely many smoothly trivial symplectic isotopy classes of exact symplectomorphisms with positive Floer-theoretic entropy on any $4n$-dimensional Liouville domain that admits an $A_2$-configuration of Lagrangian spheres. We also prove that the Floer-theoretic entropy of an exact symplectomorphism on a Liouville domain provides a lower bound for its topological entropy.

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arXiv2024

Symplectic fillings of unit cotangent bundles of spheres and applications

We prove the uniqueness, up to diffeomorphism, of symplectically aspherical fillings of the unit cotangent bundle of odd-dimensional spheres. As applications, we first show the non-existence of exact symplectic cobordisms between some 5-dimensional Brieskorn manifolds. We also determine the diffeomorphism types of closed symplectic 6-manifolds with certain codimension 2 symplectic submanifolds.

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arXiv2023

Volume growth via real Lagrangians in Milnor fibers of Brieskorn polynomials

In this paper we study the volume growth in the component of fibered twists in Milnor fibers of Brieskorn polynomials. We obtain a uniform lower bound of the volume growth for a class of Brieskorn polynomials using a Smith inequality for involutions in wrapped Floer homology. To this end, we investigate a family of real Lagrangians in those Milnor fibers whose topology can be systematically described in terms of the join construction.

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arXiv2023

Rational ruled surfaces as symplectic hyperplane sections

We study embeddability of rational ruled surfaces as symplectic hyperplane sections into closed integral symplectic manifolds. From this we obtain results on Stein fillability of Boothby--Wang bundles over rational ruled surfaces.

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arXiv2023

On dynamically convex contact manifolds and filtered symplectic homology

In this paper we are interested in characterizing the standard contact sphere in terms of dynamically convex contact manifolds which admit a Liouville filling with vanishing symplectic homology. We first observe that if the filling is flexible, then those contact manifolds are contactomorphic to the standard contact sphere. We then investigate quantitative geometry of those contact manifolds focusing on similarities with the standard contact sphere in filtered symplectic homology.

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arXiv2021

On the topology of Lagrangian fillings of the standard Legendrian sphere

In this paper we study the uniqueness of Lagrangian fillings of the standard Legendrian sphere $\mathcal{L}_0$ in the standard contact sphere $(S^{2n-1}, \xi_{\text st})$. We show that every exact Maslov zero Lagrangian filling $L$ of $\mathcal{L}_0$ in a Liouville filling of $(S^{2n-1}, \xi_{\text st})$ is a homology ball. If we restrict ourselves to real Lagrangian fillings, then $L$ is diffeomorphic to the $n$-ball for $n \geq 6$.

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arXiv2021

A computation of the ring structure in wrapped Floer homology

We give an explicit computation of the ring structure in wrapped Floer homology of a class of real Lagrangians in $A_k$-type Milnor fibers. In the $A_k$-type plumbing description, those Lagrangians correspond to the cotangent fibers or the diagonal Lagrangians. The main ingredient of the computation is to apply a version of the Seidel representation. For a technical reason, we first carry out computations in v-shaped wrapped Floer homology, and this in turn gives the desired ring structure via the Viterbo transfer map.

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arXiv2021

Equivariant wrapped Floer homology and symmetric periodic Reeb orbits

The aim of this article is to apply a Floer theory to study symmetric periodic Reeb orbits. We define positive equivariant wrapped Floer homology using a (anti-)symplectic involution on a Liouville domain and investigate its algebraic properties. By a careful analysis of index iterations, we obtain a non-trivial lower bound on the minimal number of geometrically distinct symmetric periodic Reeb orbits on a certain class of real contact manifolds. This includes non-degenerate real dynamically convex starshaped hypersurfaces in $\mathbb{R}^{2n}$ which are invariant under complex conjugation. As a result, we give a partial answer to the Seifert conjecture on brake orbits in the contact setting.

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arXiv2020

Remarks on the systoles of symmetric convex hypersurfaces and symplectic capacities

In this note we study the systoles of convex hypersurfaces in $\mathbb{R}^{2n}$ invariant under an anti-symplectic involution. We investigate a uniform upper bound of the ratio between the systole and the symmetric systole of the hypersurfaces using symplectic capacities from Floer theory. We discuss various concrete examples in which the ratio can be understood explicitly.

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arXiv2020

Bifurcations of symmetric periodic orbits via Floer homology

We give criteria for the existence of bifurcations of symmetric periodic orbits in reversible Hamiltonian systems in terms of local equivariant Lagrangian Rabinowitz Floer homology. As an example, we consider the family of the direct circular orbits in the rotating Kepler problem and observe bifurcations of torus-type orbits. Our setup is motivated by numerical work of Hénon on Hill's lunar problem.

math.DS↗
arXiv2019

Diffeomorphism type via aperiodicity in Reeb dynamics

We characterise boundary shaped disc like neighbourhoods of certain isotropic submanifolds in terms of aperiodicity of Reeb flows. We prove uniqueness of homotopy and diffeomorphism type of such contact manifolds assuming non-existence of short periodic Reeb orbits.

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arXiv2017

Volume growth in the component of fibered twists

For a Liouville domain $W$ whose boundary admits a periodic Reeb flow, we can consider the connected component $[τ] \in π_0(\text{Symp}^c(\widehat W))$ of fibered twists. In this paper, we investigate an entropy-type invariant, called the slow volume growth, of the component $[τ]$ and give a uniform lower bound of the growth using wrapped Floer homology. We also show that $[τ]$ has infinite order in $π_0(\text{Symp}^c(\widehat W))$ if there is an admissible Lagrangian $L$ in $W$ whose wrapped Floer homology is infinite dimensional. We apply our results to fibered twists coming from the Milnor fibers of $A_k$-type singularities and complements of a symplectic hypersurface in a real symplectic manifold. They admit so-called real Lagrangians, and we can explicitly compute wrapped Floer homology groups using a version of Morse-Bott spectral sequences.

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arXiv2015

Brieskorn manifolds in contact topology

In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving exotic contact structures, invariants and orderability. The main tool for the required computations is a version of the Morse-Bott spectral sequence. We provide a proof for the particular version that is useful for us.

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