Browsing by Author "Buse, Olguta"

Now showing 1 - 5 of 5
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    Chambers in the symplectic cone and stability of symplectomorphism group for ruled surface
    (arXiv, 2022-02-14) Buse, Olguta; Li, Jun; Mathematical Sciences, School of Science
    We continue our previous work to prove that for any non-minimal ruled surface $(M,\omega)$, the stability under symplectic deformations of $\pi_0, \pi_1$ of $Symp(M,\omega)$ is guided by embedded $J$-holomorphic curves. Further, we prove that for any fixed sizes blowups, when the area ratio $\mu$ between the section and fiber goes to infinity, there is a topological colimit of $Symp(M,\omega_{\mu}).$ Moreover, when the blowup sizes are all equal to half the area of the fiber class, we give a topological model of the colimit which induces non-trivial symplectic mapping classes in $Symp(M,\omega) \cap \rm Diff_0(M),$ where $\rm Diff_0(M)$ is the identity component of the diffeomorphism group. These mapping classes are not Dehn twists along Lagrangian spheres.
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    Genera of integer representations and the Lyndon-Hochschild-Serre spectral sequence
    (2021-08) Neuffer, Christopher; Ramras, Daniel; Ji, Ronghui; Morton, Patrick; Buse, Olguta
    There has been in the past ten to fifteen years a surge of activity concerning the cohomology of semi-direct product groups of the form $\mathbb{Z}^{n}\rtimes$G with G finite. A problem first stated by Adem-Ge-Pan-Petrosyan asks for suitable conditions for the Lyndon-Hochschild-Serre Spectral Sequence associated to this group extension to collapse at second page of the Lyndon-Hochschild-Serre spectral sequence. In this thesis we use facts from integer representation theory to reduce this problem to only considering representatives from each genus of representations, and establish techniques for constructing new examples in which the spectral sequence collapses.
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    Packing stability for symplectic 4-manifolds.
    (AMS, 2016-11) Buse, Olguta; Hind, Richard; Opshtein, Emmanuel; Department of Mathematical Sciences, School of Science
    The packing stability in symplectic geometry was first noticed by Biran (1997): the symplectic obstructions to embed several balls into a manifold disappear when their size is small enough. This phenomenon is known to hold for all closed manifolds with rational symplectic class, as well as for all ellipsoids. In this note, we show that packing stability holds for all closed, and several open, symplectic $ 4$-manifolds.
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    Ricci Curvature of Finsler Metrics by Warped Product
    (2020-05) Marcal, Patricia; Shen, Zhongmin; Buse, Olguta; Ramras, Daniel; Roeder, Roland
    In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.
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    Weighted Curvatures in Finsler Geometry
    (2023-08) Zhao, Runzhong; Shen, Zhongmin; Buse, Olguta; Ramras, Daniel; Roeder, Roland
    The curvatures in Finsler geometry can be defined in similar ways as in Riemannian geometry. However, since there are fewer restrictions on the metrics, many geometric quantities arise in Finsler geometry which vanish in the Riemannian case. These quantities are generally known as non-Riemannian quantities and interact with the curvatures in controlling the global geometrical and topological properties of Finsler manifolds. In the present work, we study general weighted Ricci curvatures which combine the Ricci curvature and the S-curvature, and define a weighted flag curvature which combines the flag curvature and the T -curvature. We characterize Randers metrics of almost isotropic weighted Ricci curvatures and show the general weighted Ricci curvatures can be divided into three types. On the other hand, we show that a proper open forward complete Finsler manifold with positive weighted flag curvature is necessarily diffeomorphic to the Euclidean space, generalizing the Gromoll-Meyer theorem in Riemannian geometry.