相关论文: On the parallelepipeds in algebra and topology

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…

In this paper we study the topology of cobordism categories of manifolds with corners. Specifically, if {Cob}_{d,<k>} is the category whose objets are a fixed dimension d, with corners of codimension less than or equal to k, then we…

Algebraic parabolic bundles on smooth projective curves over algebraically closed field of positive characteristic is defined. It is shown that the category of algebraic parabolic bundles is equivalent to the category of orbifold bundles…

This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…

A complete classification of a class of $3$-dimensional algebras is provided. In algebraically closed field $\mathbb{F}$ case this class is an open, dense (in Zariski topology) subset of $\mathbb{F}^{27}$.

Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…

We develop general foundations of topological algebra over a linearly topologized ring k in a format applicable to both formal schemes and analytic adic spaces. We are especially interested in determining exact closed tensor categories of…

We study certain Poisson structures related to quantized enveloping algebras. In particular, we give a description of the Poisson structure of a certain manifold associated to the ring of differential operators.

We classify proper holomorphic mappings between generalized pseudoellipsoids of different dimensions. Those domains are parametrized by the exponents. The relations among them are also obtained. Main tool is the orthogonal decomposition of…

We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.

Recent developments in ergodic theory, additive combinatorics, higher order Fourier analysis and number theory give a central role to a class of algebraic structures called nilmanifolds. In the present paper we continue a program started by…

Holomorphic manifolds over Cayley-Dickson algebras are defined and their embeddings and immersions are studied.

We classify finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero whose Hopf coradcial is isomorphic to the smallest non-pointed basic Hopf algebra, under the assumption that the diagrams are strictly…

We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety…

We study degree one maps between closed orientable 4-manifolds with cyclic $\pi_1$, and obtain some results on the existence and finiteness, as well as some relation of $1$-domination and Euler Characteristics.

Our main theorem classifies the Auslander-Reiten triangles according to properties of the morphisms involved. As a consequence, we are able to compute the mapping cone of an irreducible morphism. We finish by showing a technique for…

We construct membrane homology groups $\h(M)$ associated with each compact connected oriented smooth manifold, and show that $\h(M)$ is matrix graded algebra.

Directed Algebraic Topology studies spaces equipped with a form of direction, to include models of non-reversible processes. In the present extension we also want to cover critical processes, indecomposable and unstoppable. The previous…

In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…