Related papers: Exotic Differentiable Structures and General Relat…
We extend our exploration of nonstandard continuum quantum field theories in 2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
Special geometry is most known from 4-dimensional N=2 supergravity, though it contains also quaternionic and real geometries. In this review, we first repeat the connections between the various special geometries. Then the constructions are…
We prove that there exist diffeomorphisms of tori, supported in a disc, which are not isotopic to symplectomorphisms with respect to any symplectic structure. This yields a partial negative answer to a question of Benson and Gordon about…
Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…
We introduce the Euler-Lagrange cohomology to study the symplectic and multisymplectic structures and their preserving properties in finite and infinite dimensional Lagrangian systems respectively. We also explore their certain difference…
Systems of ordinary differential equations (or dynamical forms in Lagrangian mechanics), induced by embeddings of smooth fibered manifolds over one-dimensional basis, are considered in the class of variational equations. For a given…
Fold maps are fundamental tools in the theory of singularities of differentiable maps and its applications to geometry. They are higher dimensional variants of Morse functions. Classes of special generic maps and round fold maps are…
Several papers have been written studying unexpected hypersurfaces. We say a finite set of points Z admits unexpected hypersurfaces if a general union of fat linear subspaces imposes less that the expected number of conditions on the ideal…
The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…
Skew-symmetric forms possess unique capabilities. The properties of closed exterior and dual forms, namely, invariance, covariance, conjugacy and duality, either explicitly or implicitly appear in all invariant mathematical formalisms. This…
Hydrodynamics is shown to induce non-Hermitian topological phenomena in ordinary, passive soft matter. This is demonstrated for the first time by subjecting a 2D elastic lattice to a low-Reynolds viscous flow. The interplay of hydrodynamics…
Despite remarkable success in describing supergravity reductions and backgrounds, generalized geometry and the closely related exceptional field theory are still lacking a fundamental object of differential geometry, the Riemann tensor. We…
The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at…
Models that involve extra dimensions have introduced completely new ways of looking up on old problems in theoretical physics. The aim of the present notes is to provide a brief introduction to the many uses that extra dimensions have found…
In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure…
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
Skew-symmetric differential forms play an unique role in mathematics and mathematical physics. This relates to the fact that closed exterior skew-symmetric differential forms are invariants. The concept of "Exterior differential forms" was…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…
In accordance with recent progress of fracton topological phases, unusual topological phases of matter hosting fractionalized quasiparticle excitations with mobility constraints, new type of symmetry is studied -- multipole symmetry,…