Related papers: Filtered complexes and cohomologically equivalent …

We introduce the notion of weak reduciblity for Dupin submanifolds with arbitrary codimension. We give a complete characterization of all weakly reducible Dupin submanifolds, as a consequence of a general result on a broader class of…

Let $(R, \frak m)$ be a homomorphic image of a Cohen-Macaulay local ring and $M$ a finitely generated $R$-module. We use the splitting of local cohomology to shed a new light on the structure of non-Cohen-Macaulay modules. Namely, we show…

Let $X$ be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on $X$ by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction…

The coprimary filtration is a basic construction in commutative algebra. In this article, we prove the existence and uniqueness of coprimary filtration of modules (not necessarily finitely generated) over a Noetherian ring. Moreover, we…

For a flat $p$-adic formal family $S$ of log points over a complete discrete valuation ring with perfect residue field of mixed characteristics $(0,p)$ and for a simple normal crossing log scheme $X$ over an exact closed log subscheme of…

We construct Hamiltonian Floer complexes associated to continuous, and even lower semi-continuous, time dependent exhaustion functions on geometrically bounded symplectic manifolds. We further construct functorial continuation maps…

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many…

We characterize general pseudo-harmonic morphisms from a Riemannian manifold to a Hermitian manifold as pseudo horizontally weakly conformal maps with an additional property. We study to what extent we can (locally) describe these…

The class of the hypercomplex pseudo-Hermitian manifolds is considered. The flatness of the considered manifolds with the 3 parallel complex structures is proved. Conformal transformations of the metrics are introduced. The conformal…

Let X be a topological space, and let C(X) be the complex of singular cochains on X with real coefficients. We denote by Cc(X) the subcomplex given by continuous cochains, i.e. by such cochains whose restriction to the space of simplices…

We compare several different notions of filtered derived commutative ring, discussing HKR-filtered Hochschild homology, Hodge-filtered de Rham cohomology, and the lesser-known Hodge-filtered infinitesimal cohomology. Our main result is that…

The space $\Gamma_X$ of all locally finite configurations in a Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $\Gamma_X$, equipped with the Poisson measure, and the…

In this work, merging ideas from compatible discretisations and polyhedral methods, we construct novel fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra. The spaces and operators that appear in these…

Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…

It is well known that the validity of the so called Lenard-Magri scheme of integrability of a bi-Hamiltonian PDE can be established if one has some precise information on the corresponding 1st variational Poisson cohomology for one of the…

The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…

In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford…

Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of…

For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has…

Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.