Given a smooth compact Riemannian manifold M and a Hamiltonian H on the cotangent space T∗M , strictly convex and superlinear in the momentum variables, we prove uniqueness of certain “ergodic” invariant Lagrangian graphs within a given homology or cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our result implies global uniqueness of Lagrangian KAM tori...

In this paper, deformations of L∞-algebras are defined in such a way that the bases of deformations are L∞-algebras, as well. A universal and a semiuniversal deformation is constructed for L∞-algebras, whose cotangent complex admits a splitting. The paper also contains an explicit construction of a minimal L∞-structure on the homology H of a differential graded Lie algebra L and of an L∞-quasi-...

We introduce an integral form U of the quantized enveloping algebra of sl2. The algebra U is just large enough so that the quasi-R-matrix is contained in a completion of U ⊗ U . We study several completions of the algebra U , and determine their centers. This study is motivated by a study of integrality properties of the quantum sl2 invariants of links and integral homology spheres.

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.

Geometric aspects of the filtration on classical links by k-quasi-isotopy are discussed, including the effect of Whitehead doubling and relations with Smythe's n-splitting and Kobayashi's k-contractibility. One observation is: ω-quasi-isotopy is equivalent to PL isotopy for links in a homotopy 3-sphere (resp. contractible open 3-manifold) M if and only if M is homeomorphic to S 3 (resp. R 3). A...

in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

Setting of this paper is Bishop's constructive mathematics. For a relation σ on a set with apartness is called quasi-antiorder if it is consistent and cotransitive. The quasi-antiorder σ is complete if holds . 0 1 / = σ σ − ∩ In this paper the following assertion ‘A quasi-antiorder is the intersection of a collection of quasi-antiorders.’ is given.

We survey recent results on inequalities between the ranks of homotopy and cohomology groups (resp., graded components mixed Hodge structures these groups) for rationally elliptic spaces quasi-projective varieties which are elliptic). also discuss a refinement describing new invariant allowing to compare homology groups. Its definition is based study range parameter r such that rP(t)<Q(t)r all ...

We realise Stroppel’s extended arc algebra \[13, 51] in the Fukaya–Seidel category of a natural Lefschetz fibration on generic fibre adjoint quotient map type $A$ nilpotent slice with two Jordan blocks, and hence obtain symplectic interpretation certain parabolic two-block versions Bernstein–Gel’fand–Gel’fand $\\mathcal{O}$. As an application, we give new geometric construction spectral sequenc...