24,246 research outputs found
Smooth constructions of homotopy-coherent actions
No full textWe prove that, for nice classes of infinite-dimensional smooth groups
G
, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of
G
. This yields a bridge between infinite-dimensional smooth groups and homotopy theory.
The result relies on two computations: one showing that the diffeological homotopy groups of the Milnor classifying space
B
G
are naturally equivalent to the (continuous) homotopy groups, and a second showing that a particular strict category localizes to yield the homotopy type of
B
G
.
We then prove a result in symplectic geometry: these methods are applicable to the group of Liouville automorphisms of a Liouville sector. The present work is written with an eye toward Oh and Tanaka (2019), where our constructions show that higher homotopy groups of symplectic automorphism groups map to Fukaya-categorical invariants, and where we prove a conjecture of Teleman from the 2014 ICM in the Liouville and monotone settings.11Nsciescopu
ANALYSIS OF CONTACT CAUCHY-RIEMANN MAPS II: CANONICAL NEIGHBORHOODS AND EXPONENTIAL CONVERGENCE FOR THE MORSE-BOTT CASE
No full textThis is a sequel to the papers Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43-63, eds. by Y.-J. Suh and et al. for ICM-2014 satellite conference, Daejeon, Korea, August 2014; arXiv:1212.4817; Analysis of contact Cauchy-Riemann maps I: a priori C-k estimates and asymptotic convergence, submitted, preprint, 2012, arXiv:1212.5186v3). In Oh and Wang (Real and Complex Submanifolds, Springer Proceedings in Mathematics and Statistics 106 (2014), 43-63, eds. by Y.-J. Suh and et al. for ICM-2014 satellite conference, Daejeon, Korea, August 2014; arXiv:1212.4817), the authors introduced a canonical affine connection on M associated to the contact triad (M, lambda, J). In Oh and Wang (Analysis of contact Cauchy-Riemann maps I: a priori C-k estimates and asymptotic convergence, submitted, preprint, 2012, arXiv:1212.5186v3), they used the connection to establish a priori W-k'P-coercive estimates for maps w : Sigma -> M satisfying(pi) w = 0, d(w*lambda o j) = 0 without involving symplectization. We call such a pair (w, j) a contact instanton. In this paper, we first prove a canonical neighborhood theorem of the locus Q foliated by closed Reeb orbits of a Morse-Bott contact form. Then using a general framework of the three-interval method, we establish exponential decay estimates for contact instantons (w, j) of the triad (M, lambda, J), with lambda a Morse-Bott contact form and J a CR-almost complex structure adapted to Q, under the condition that the asymptotic charge of (w, j) at the associated puncture vanishes. We also apply the three-interval method to the symplectization case and provide an alternative approach via tensorial calculations to exponential decay estimates in the Morse-Bott case for the pseudoholomorphic curves on the symplectization of contact manifolds. This was previously established by Bourgeois (A Morse-Bott approach to contact homology, Ph.D. dissertation, Stanford University, 2002) (resp. by Bao (On J-holomorphic curves in almost complex manifolds with asymptotically cylindrical ends, Pacific J. Math. 278(2) (2015), 291-324)), by using special coordinates, for the cylindrical (resp. for the asymptotically cylindrical) ends. The exponential decay result for the Morse-Bott case is an essential ingredient in the setup of the moduli space of pseudoholomorphic curves which plays a central role in contact homology and symplectic field theory (SFT).11Nsciescopu
Deformations of Coisotropic Submanifolds in Jacobi Manifolds
No full textIn this paper, we attach an L∞-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), Lê-Oh (locally conformal symplectic case). As a new special case, we attach an L∞-algebra to any coisotropic submanifold in a contact manifold. The L∞-algebra of a coisotropic submanifold S governs the (formal) deformation problem of S
Exact Lagrangian submanifolds, Lagrangian spectral invariants and Aubry-Mather theory
Get PDFWe construct graph selectors for compact exact Lagrangians in the cotangent
bundle of an orientable, closed manifold. The construction combines Lagrangian
spectral invariants developed by Oh and results by Abouzaid about the Fukaya
category of a cotangent bundle. We also introduce the notion of Lipschitz-exact
Lagrangians and prove that these admit an appropriate generalization of graph
selector. We then, following Bernard-Oliveira dos Santos, use these results to
give a new characterization of the Aubry and Mane sets of a Tonelli Hamiltonian
and to generalize a result of Arnaud on Lagrangians invariant under the flow of
such Hamiltonians.Comment: v4: final version; to appear in Math. Proc. Camb. Phil. So
A critical point analysis of Landau-Ginzburg potentials with bulk in Gelfand-Cetlin systems
No full text© 2021 by Kyoto University.Using the bulk deformation of Floer cohomology by Schubert classes and non-Archimedean analysis of Fukaya-Oh-Ohta-Ono's bulk-deformed potential function, we prove that every complete flag manifold Fl(n) (n ≥ 3) with a monotone Kirillov-Kostant-Souriau (KKS) symplectic form carries a continuum of nondisplaceable Lagrangian tori which degenerates to a nontorus fiber in the Hausdorff limit. In particular, the Lagrangian S3-fiber in Fl(3) is nondisplaceable, answering a question raised by Nohara and Ueda who computed its Floer cohomology to be vanishing.11Nsciescopu
Construction of a linear K-system in Hamiltonian Floer theory
No full text© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.The notion of linear K-system was introduced by the present authors as an abstract model arising from the structure of compactified moduli spaces of solutions to Floer’s equation in the book (Fukaya et al. in Springer monographs in mathematics, Springer, Berlin, 2020). The purpose of the present article is to provide a geometric realization of the linear K-system associated with solutions to Floer’s equation in the Morse–Bott setting. Immediate consequences [when combined with the abstract theory from Fukaya et al. (Springer monographs in mathematics, Springer, Berlin, 2020)] are the construction of Floer cohomology for periodic Hamiltonian systems on general compact symplectic manifolds without any restriction, and the construction of an isomorphism over the Novikov ring between the Floer cohomology and the singular cohomology of the underlying symplectic manifold. The present article utilizes various analytical results on pseudoholomorphic curves established in our earlier papers and books. However, the paper itself is geometric in nature, and does not presume much prior knowledge of Kuranishi structures and their construction but assumes only the elementary part thereof, and results from Fukaya et al. (Surv Differ Geom 22:133–190, 2018) and Fukaya et al. (Exponential decay estimate and smoothness of the moduli space of pseudoholomorphic curves) on their construction, and the standard knowledge on Hamiltonian Floer theory. We explain the general procedure of the construction of a linear K-system by explaining in detail the inductive steps of ensuring the compatibility conditions for the system of Kuranishi structures leading to a linear K-system for the case of Hamiltonian Floer theory.11Nsciescopu
Continuous Hamiltonian dynamics and area-preserving homeomorphism group of D2
Get PDFThe main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group {\rm Homeo}^\Omega(D^2,\del D^2) of area preserving homeomorphisms of the 2-disc . We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism \Cal: {\rm Diff}^\Omega(D^1,\del D^2) \to \R to a homomorphism \overline \Cal: {\rm Hameo(}D^2,\del D^2) \to \R to that of the vanishing of the basic phase function , a Floer theoretic graph selector constructed in \cite{oh:jdg}, that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian on that is obtained via the natural embedding . Here {\rm Hameo(}D^2,\del D^2) is the group of Hamiltonian homeomorphisms introduced by M\"uller and the author \cite{oh:hameo1}. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of \emph{weakly graphical} topological Hamiltonian loops on via a study of the associated Hamiton-Jacobi equation.1111Ysciescopuskc
Tunicamycins from Marine-Derived Streptomyces bacillaris Inhibit MurNAc-Pentapeptide Translocase in Staphylococcus aureus
No full textFour tunicamycin class compounds, tunicamycin VII (1), tunicamycin VIII (2), corynetoxin U17a (3), and tunicamycin IX (4), were isolated from the culture broth of the marine-derived actinomycete Streptomyces sp. MBTG32. The strain was identified using the 16S rDNA sequencing technique, and the isolated strain was closely related to Streptomyces bacillaris. The structures of the isolated compounds were elucidated based on spectroscopic data and comparisons with previously reported NMR data. Compounds 1–4 showed potent antibacterial activities against Gram-positive bacteria, especially Staphylococcus aureus, with MIC values of 0.13–0.25 µg/mL. Through a recombinant enzyme assay and overexpression analysis, we found that the isolated compounds exerted potent inhibitory effects on S. aureus MurNAc-pentapeptide translocase (MraY), with IC50 values of 0.08–0.21 µg/mL. The present results support that the underlying mechanism of action of tunicamycins isolated from marine-derived Streptomyces sp. is also associated with the inhibition of MraY enzyme activity in S. aureus.Y
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