記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：World Scientific Pub Co Pte Ltd  

Many transformation groups of manifolds are simple, but their universal coverings are not. In this paper, we study the concept of relatively simple group, that is, a group with the maximum proper normal subgroup. We show that many examples of universal coverings of transformation groups are relatively simple, including the universal covering [Formula: see text] of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold [Formula: see text]. Tsuboi constructed a metric space [Formula: see text] for a simple group [Formula: see text]. We generalize his construction to relatively simple groups, and study their large-scale geometric structure. In particular, Tsuboi’s metric space of [Formula: see text] is not quasi-isometric to the half-line for every closed symplectic manifold [Formula: see text].

DOI： 10.1142/s1793525326500445

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Tokyo Journal of Mathematics  

DOI： 10.3836/tjm/1502179420

arXiv

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：Mathematical Society of Japan (Project Euclid)  

DOI： 10.2969/jmsj/84278427

arXiv

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記述言語：英語   掲載種別：研究論文（学術雑誌）   出版者・発行元：World Scientific Pub Co Pte Lt  

In this paper, we introduce the notion of pseudoheaviness of closed subsets of closed symplectic manifolds and prove the existence of pseudoheavy fibers of moment maps. In particular, we generalize Entov and Polterovich’s theorem, which ensures the existence of non-displaceable fibers. As its application, we provide a partial answer to a problem posed by them, which asks the existence of heavy fibers. Moreover, we obtain a family of singular Lagrangian submanifolds in [Formula: see text] with various rigidities.

DOI： 10.1142/s0219199720500479

arXiv

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

We show that the presence of a non-contractible one-periodic orbit of a
Hamiltonian diffeomorphism of a connected closed symplectic manifold
$(M,\omega)$ implies the existence of infinitely many non-contractible simple
periodic orbits, provided that the symplectic form $\omega$ is aspherical and
the fundamental group $\pi_1(M)$ is either a virtually abelian group or an
$\mathrm{R}$-group. We also show that a similar statement holds for Hamiltonian
diffeomorphisms of closed monotone or negative monotone symplectic manifolds
under the same conditions on their fundamental groups. These results generalize
some works by Ginzburg and G\"urel. The proof uses the filtered Floer--Novikov
homology for non-contractible periodic orbits.

DOI： 10.4310/JSG.2019.v17.n6.a9

arXiv

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記述言語：日本語

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DOI： 10.48550/arXiv.2504.16962

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その他リンク： https://arxiv.org/pdf/2504.16962

In this paper, we show that the pointwise finite-dimensional two-parameter
persistence module $\mathbb{HF}_*^{(\bullet,\bullet]}$, defined in terms of
interlevel filtered Floer homology, is rectangle-decomposable. This allows for
the definition of a barcode $\mathcal{B}_*^{(\bullet,\bullet]}$ consisting only
of rectangles in $\mathbb{R}^2$ associated with
$\mathbb{HF}_*^{(\bullet,\bullet]}$. We observe that this rectangle barcode
contains information about Usher's boundary depth and spectral invariants
developed by Oh, Schwarz, and Viterbo. Moreover, we establish relevant
stability results, particularly concerning the bottleneck distance and Hofer's
distance.

arXiv

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その他リンク： http://arxiv.org/pdf/2312.07847v4

対象： 高校生

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