Related papers: Residues for maps generically transverse to distri…

We establish Thom's jet transversality theorem for regular maps from an affine algebraic manifold to an algebraic manifold satisfying a suitable flexibility condition. It can be considered as the algebraic version of Forstneri\v{c}'s jet…

We provide combinatorial/topological formula for the multiplicity of a complex analytic normal surface singularity whenever the analytic structure on the fixed topological type is generic.

This paper is about the study of F-transforms based on overlap and grouping maps, residual and co-residual implicator over complete lattice from both constructive and axiomatic approaches. Further, the duality, basic properties, and the…

We review some definitions and basic notions relating to generalised spin structures and introduce the notion of reducibility. We discuss connections on these structures, define a covariant Lie derivative for associated bundles and develop…

Let f be a generic polynomial mapping mapping from the plane to the plane. There are constructed quadratic forms whose signatures determine the number of positive and negative cusps of f.

We derive explicit formulas for the inverses of the Cartan matrices of the simple Lie algebras and the basic classical Lie superalgebras, as well as for their infinite generalizations.

The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…

A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in…

We introduce a Whitney polynomial for hypermaps and use it to generalize the results connecting the circuit partition polynomial to the Martin polynomial and the results on several graph invariants.

Let f: X -> Z be a separated essentially-finite-type flat map of noetherian schemes, and \delta: X --> X \times_Z X the diagonal map. The fundamental class C_f (globalizing residues) is a map from the relative Hochschild functor…

We derive residue formulas for the regularized integrals (introduced by Li-Zhou) on configuration spaces of elliptic curves. Based on these formulas, we prove that the regularized integrals satisfy holomorphic anomaly equations, providing a…

In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…

In his celebrated paper "Generic projections", John Mather has shown that almost all linear projections from a submanifold of a vector space into a subspace are transverse with respect to a given modular submanifold. In this paper, an…

An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…

We consider manifolds whose transition maps are restrictions of polynomial mappings $\mathbb{R}^n\to\mathbb{R}^n$, and use them to give an equivalent statement of the Jacobian conjecture over the real field.

Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…

The generalized Verlinde formulae expressing traces of mapping classes corresponding to automorphisms of certain Riemann surfaces, and the congruence relations on allowed modular representations following from them are presented. The…

A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…

We study the group of volume-preserving diffeomorphisms on a manifold. We develop a general theory of implicit generating forms. Our results generalize the classical formulas for generating functions of symplectic twist maps.

In this paper, we consider the scalar reaction-diffusion equations $\partial_t u=\Delta u + f(x,u,\nabla u)$ on a bounded domain $\Omega\subset\mathbb{R}^d$ of class $C^2$. We show that the heteroclinic and homoclinic orbits connecting…