Related papers: Indices of quaternionic complexes

A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…

We consider a classical N. Steenrod's problem on realization of homology classes by images of the fundamental classes of manifolds. It is well-known that each integral homology class can be realized with some multiplicity as an image of the…

Since variational symplectic integrators for the guiding center was proposed [1,2], structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli…

We present an explicit basis for orders of arbitrary level N>1 in definite rational quaternion algebras. These orders have applications to computations of spaces of elliptic and quaternionic modular forms.

Let $\Lambda$ be a smooth Lagrangian submanifold of a complex symplectic manifold $X$. We construct twisted simple holonomic modules along $\Lambda$ in the stack of deformation-quantization modules on $X$.

This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…

We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In particular, we explain in detail how closed, simply…

We give a classification of the matrices in the unitary group U(1,1;H),where H is the division ring of the real quaternions. To this end, we consider the complex representation phi(P) for P in U(1,1;H). Next, we compute the characteristic…

First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…

The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…

We present an algorithm for the construction of lower dimensional elliptic tori in parametric Hamiltonian systems by means of the parametrization method with the tangent and normal frequencies being prescribed. This requires that the…

We initiate the study of the generalized quaternionic manifolds by classifying the generalized quaternionic vector spaces, and by giving two classes of nonclassical examples of such manifolds. Thus, we show that any complex symplectic…

We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperk\"ahler are analogs of the…

We develop a general method to calculate entropy numbers of standard Sobolev's classes on an arbitrary compact homogeneous Riemannian manifold. Our method is essentially based on a detailed study of geometric characteristics of norms…

This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that on an affine quaternionic manifold there is one and only one…

We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…

Let $\mathcal{M}(n,m;\F \bp^n)$ be the configuration space of $m$-tuples of pairwise distinct points in $\F \bp^n$, that is, the quotient of the set of $m$-tuples of pairwise distinct points in $\F \bp^n$ with respect to the diagonal action…

Several sets of quaternionic functions are described and studied with respect to hy-perholomorphy, addition and (non commutative) multiplication, on open sets of H, then Hamil-ton 4-manifolds analogous to Riemann surfaces, for H instead of…

In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of the function spaces and the geometry of the underlining spaces are intertwined. After briefly…